Trigonometric Functions

pls help and be sure to show all your work !! the second pic is the graph that needs to be plotted for the first question.

The evaluation of the matrix multiplication can be presented as follows;

Question #1

The matrix M and A are;

[tex]M=\begin{bmatrix}1 &14 &24 &19 &14 &1&5 \\7 &20 &0 &0 &0 &14 &18\\5 &0 &9 &9 &4 &7 &0 \\\end{bmatrix}[/tex]

[tex]A = \begin{bmatrix} 1& 2 &3 \\3 & 1 & 2 \\ 2 & 3& 1 \\\end{bmatrix}[/tex]

The encoded message in matrix form is therefore;

[tex]A\times M=\begin{bmatrix}30 &54 &51 &46 &26 &50&41 \\20 &62 &90 &75 &50 &31&33 \\28 & 88 &57 &47 &32 &51&64 \\\end{bmatrix}[/tex]

The encoded message is;  30   20   28   54   62   88   51   90   57   46   75   47   26   50   31   51   41   33   64

Question #2

The matrices M and A × M are;

[tex]M=\begin{bmatrix}3 &16 &26 &21 &16 &3 &7\\9 & 22 & 0 &0 &0 &16&20 \\7 &0 &11 &11 &6 &9 &0\\\end{bmatrix}[/tex]

[tex]A\times M=\begin{bmatrix}42 &60 &59 &54 &34 &62&47 \\32 & 70 & 100 &85 &60 &43&41 \\40 & 98 & 63 &53 &38 &63 &74\\\end{bmatrix}[/tex]

The encoded message is; [tex]{}[/tex]42   32   40   60   70   98   59   100   63   54   85   53   34   60   38   62   43   63   47   41   74

The rule for matrix multiplication is that the number of columns in the first matrix should be the same as the number of rows in the second matrix

A m by n matrix can only multiply a n by p matrix to produce a m by p matrix

The matrix M for the message can be presented as follows;

The letters are replaced with the corresponding numbers to get;

[tex]{}[/tex]1  7  5   14   20  0  24  0  9    19   0   9   14   0   4   1   14   7   5   18   0

M = [tex]\begin{bmatrix}1 &14 &24 &19&14&1 &5 \\7 & 20 &0 &0 &0&14&18\\5 & 0& 9 & 9&4&7&0\\\end{bmatrix}[/tex]

The matrix A is presented as follows;

[tex]A=\begin{bmatrix}1 & 2 & 3 \\3 & 1 & 2 \\ 2& 3 &1 \\\end{bmatrix}[/tex]

Therefore;

[tex]A \times M = \begin{bmatrix}30 &54 &51 &46&26&50 &41 \\20 & 62 &90 &75 &50&31&33\\28 & 88& 57 & 47&32&51&64\\\end{bmatrix}[/tex]

The encoded message is therefore;

Question #2

The 2-letter circular shift indicates that the message becomes;

AGENT X IS IN DANGER

The above message becomes;

CIGPV Z KU KO FCOIGT

The numbers comes;

[tex]{}[/tex]3  9  7  16   22  0  26   0   11  21  0  11   15  0  6  3   15   9   7   20

The Matrix Mis therefore;

[tex]M = \begin{bmatrix}3 &16 &26 &21&16&3 &7 \\9 & 22 &0 &0 &0&16&20\\7 & 0& 11 & 11&6&9&0\\\end{bmatrix}[/tex]

The message becomes;

[tex]A \times M = \begin{bmatrix}42 &60 &59 &54&34&62 &47 \\32 & 70 &100 &85 &60&43&41\\40 & 98& 63 & 53&38&63&74\\\end{bmatrix}[/tex]

The encoded message is; [tex]{}[/tex] 42  32   40   60   70   98   59   100   63   54   85   53   34   60   38   62   43   63   47   41   74

The information in the attached file related to the question includes;

Two agents are to send a confidential message which is to be encoded using a 3 × 3 invertible matrix A that consists of natural number elements.  The coding strategy consists of replacing each letter by the number representing the letter in the alphabet, after which the numbers representing the letters are placed in columns of 3 elements, completing the missing elements in the last column and blanks with zero in the matrix M. See above.

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Answer:

Step-by-step explanation:

[tex]\frac{30\sqrt{2^{4n-2} +2^{4n+1} } }{(3^{n} +3^{n+1} )^2} \\=\frac{30\sqrt{2^{4n} *2^{-2} +2^{4n} *2^{1} } }{3^{2n} (1+3^{1}) } \\=\frac{30*2^{2n} \sqrt{\frac{1}{2^{2} }+2 } }{4*3^{2n} } \\=\frac{30*2^{2n}*\frac{3}{2} }{4*3^{2n} } \\=\frac{45(2^{2} )^{n} }{4(3^{2} )^{n} } \\=\frac{45}{4} *(\frac{4}{9} )^{n} \\[/tex]

it is a G.P. with common ratio r=4/9 <1

[tex]s=\frac{a}{1-r} ,a=first~term\\s=\frac{\frac{45}{4} *(\frac{16}{81} )}{1-\frac{4}{9} } [by~n=2]\\s=\frac{20}{9} *\frac{9}{5} \\=4[/tex]

Answer:

hope it is correct

Step-by-step explanation:

Since QUOR is a parallelogram, it means that opposite angles are congruent. Therefore, we have:

∠Q = ∠O and ∠UQA + ∠O = 180°

Since CD || RO, we have:

∠ORA = ∠O and ∠BUQ + ∠Q = 180°

Combining these equations, we get:

∠UQA + ∠BUQ + ∠ORA = 360°

Since ∠BUQ + ∠Q = 180°, we have:

∠BUQ = 180° - ∠Q

Substituting this into the previous equation, we get:

∠UQA + (180° - ∠Q) + ∠O = 360°

Simplifying, we get:

∠UQA = ∠Q - ∠O

Since ∠Q = ∠O (because QUOR is a parallelogram), we have:

∠UQA = 0°

Therefore, none of the given angles (A) ∠BAR, (B) ∠BUQ, or (C) ∠ORA is congruent to ∠UQA.

Answer:

(6/x) - (5y)

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In response to the stated question, we may respond that Given that she is an M, the probability that the chosen female is both a M and a C is 0.6.

Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.

a) The girl has a 0.65 chance of being a Clothes Pony (C).

b) The girl has a 50% chance of being a Makeup Missie (M).

c) The girl has a 0.30 chance of being both a Clothing Pony and a Makeup Missie.

d) Using the conditional probability formula, we can calculate the likelihood that the chosen female is both a M and a C provided that she is a M:

P(C|M) = P(C and M) divided by P (M)

Part (c) tells us that P(C and M) = 0.30, while Part (b) tells us that P(M) = 0.50. Therefore:

P(C|M) = 0.30 / 0.50 = 0.6

Given that she is an M, the likelihood that the chosen female is both a M and a C is 0.6.

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Using matrices, we can find that the products of EH and FG are defined, the rest does not satisfy.

A matrix is a rectangular array of values that are defined for mathematical operations including addition, subtraction, and multiplication.

The quantity of rows and columns in a matrix—also referred to as the order of the matrix—determines its size. A 6 4 symbol and 6 by 4 reading are used to symbolise and denote the order of a matrix having 6 rows and 4 columns.

Here in the question,

When the matrices, E and H are multiplied, the resulting matrix is a defined matrix.

Similarly, we can see when F and G are multiplied, the resulting matrix is a defined matrix.

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Answer:

15.8823% error

Step-by-step explanation:

Percent Error Formula

abs([tex]\frac{(a-x)}{x}[/tex]) * 100%

abs:  absolute value

a:  actual value

x:  expected value

Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%

                       = abs(-0.158823) * 100%

                       15.8823% error

a) The value of Hy = 1.15

b) The proportion of cartons with less than 1.15 broken eggs is 0.60

c) The answer is B)This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like.

(a) Hy = 0.67, which means that on average, there are 0.67 broken eggs per carton.

Hy = (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1

= 0.67

(b) The proportion of cartons with less than 0.67 broken eggs is 0.60 which is probability of 0 broken eggs.. This may be surprising as the probability of having less than 0.67 broken eggs is only 0.60, but this is due to the fact that the distribution is skewed towards higher values.

(c) Hy is not equal to the simple average of 0, 1, 2, 3, and 4 because the distribution is not symmetrical. The probabilities are weighted towards higher values, which increases the mean. Additionally, the value of zero should be included in the calculation, as it represents a possible outcome. Therefore, the correct formula for Hy is (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1 = 0.67.

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--The question is incomplete, answering to the question below--

"Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs.

y 0 1 2 3 4

p(y) 0.60 0.20 0.15 0.03 0.02

(a) Calculate and interpret Hy  

(b) In the long run, for what proportion of cartons is the number of broken eggs less than Hy? (Round your answer to two decimal places).

Does this surprise you?

Yes

No

(c) Explain why Hy is not equal to (0 + 1 + 2 + 3 + 4)/5 = 2.0.  

A. This computation of the mean is incorrect because the value in the denominator should equal the maximum y value.

B. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like

C. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when

D. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs."

Answer:

Step-by-step explanation:

[tex]tanx=\frac{15}{18}[/tex]     (tan is opposite/adjacent     SOHCAHTOA)

[tex]x=tan^{-1}(\frac{15}{18}) = 39.8[/tex]

Michelle would earn about $807.69 per week if she took the clerk job, rather than the administration job.

Earnings refer to the amount of money that an individual or entity has earned or generated through its business activities or work. In the context of an individual, earnings usually refer to the amount of money that a person receives as compensation for their work, such as salaries, wages, commissions, tips, bonuses, or any other form of payment for services rendered.

Earnings can also refer to the amount of money that a company generates from its business activities, such as sales revenue, profits, or earnings per share. This information is often used by investors, analysts, and other stakeholders to evaluate the financial performance of a company and make investment decisions.

To calculate Michelle's weekly earnings if she took the clerk job, we need to first calculate her biweekly earnings:

42,000 / 26 = 1,615.38 (her biweekly earnings as a clerk)

To find her weekly earnings, we can divide this number by 2:

1,615.38 / 2 = 807.69 (her weekly earnings as a clerk)

To find out how much she would earn per week if she took the administration job, we can simply divide the annual salary by the number of weeks in a year:

853 / 52 = 16.40 (her weekly earnings as an administrator)

Therefore, Michelle would earn about $807.69 per week if she took the clerk job, rather than the administration job.

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Answer:

The store with a 40% off sale.

Step-by-step explanation:

Since 1/3 of 100% is approximate, 33.4% and 40% will obviously be better. The 40% off sale is better by approximately 6.6%.

The first rational expression is 63m²+20m−32. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), first we need to find the LCD (Lowest Common Denominator) of both terms. So, we need to multiply each numerator and denominator of the first rational expression by (3m−4)(m+8)(m−7).

In the numerator, we need to multiply 63m² by (3m−4)(m+8)(m−7):

63m² × (3m−4)(m+8)(m−7) = 63m³ - 224m² + 784m - 504

In the denominator, we need to multiply 1 by (3m−4)(m+8)(m−7):

1 × (3m−4)(m+8)(m−7) = 3m³ - 12m² + 24m - 16

Therefore, the rewritten rational expression is:

63m³ - 224m² + 784m - 504/3m³ - 12m² + 24m - 16

The second rational expression is 3m³m²−25m+28. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), we first need to find

Answer:

-2 squared+3+1=0

I hope it helps

Answer:

Y = 4

Step-by-step explanation:

given x varies inversely as y then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition x = 10 when y = 6 , then

6 = [tex]\frac{k}{10}[/tex] ( multiply both sides by 10 )

60 = k

y = [tex]\frac{60}{x}[/tex] ← equation of variation

when x = 15 , then

y = [tex]\frac{60}{15}[/tex] = 4

Answer:

38%

Step-by-step explanation:

I learned in class on Friday.

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

[tex]0.38\times \dfrac{100}{100}[/tex]

[tex]= (0.38 \times 100) \times \dfrac{1}{100} =\dfrac{38}{100}[/tex]

Write in percentage notation: 38%

the Fourier series solution is not directly used to find the general solution but is used as a part of it, along with the radial solution. The Fourier series solution helps in finding the solution to the given boundary value problem, which, when combined with the radial solution, gives the complete solution to the Laplace equation.

The Fourier series approach that you have used helps in finding the solution to the boundary value problem, i.e., finding u(a,ϕ) for the given boundary conditions. However, to find a general solution to the Laplace equation, we need to use the superposition principle, which states that the sum of any two solutions to the Laplace equation is also a solution.

Therefore, we can use the previously obtained Fourier series solution for u(a,ϕ) as a building block to construct the general solution. We know that the Laplace equation has radial symmetry, which means that the temperature distribution is only a function of radius (rho) and not of angle (ϕ). Hence, we can write the general solution as:

u(rho,ϕ) = f(rho) + u(a,ϕ)

where f(rho) is the radial component of the solution and u(a,ϕ) is the previously obtained Fourier series solution.

To find f(rho), we need to solve the radial ODE using the boundary conditions at rho=0 and rho=a. Once we have obtained f(rho), we can add it to u(a,ϕ) to get the general solution.

Therefore, the Fourier series solution is not directly used to find the general solution but is used as a part of it, along with the radial solution. The Fourier series solution helps in finding the solution to the given boundary value problem, which, when combined with the radial solution, gives the complete solution to the Laplace equation.

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The temperature decreased by 41°F during the overnight hours.

Physical quantities with merely magnitude and no direction are called scalar quantities. Scalar values encompass things like mass, volume, temperature, and time. Real numbers, such as positive or negative integers or decimals, are frequently used to represent scalar quantities in mathematics.

In contrast, a vector quantity is a physical quantity that possesses both magnitude and direction. The terms displacement, velocity, force, and acceleration are all examples of vector quantities. Typically, vector values are represented by a number or symbol for the magnitude and an arrow or boldface letter for the direction.

Given that, the temperature went from 28 to -13.

The expression that represent this change are:

Expression 1: -13°F - 28°F

Expression 2: | -13°F - 28°F |

The temperature change can be calculated as:

| -13°F - 28°F | = |-41°F| = 41°F

Hence, the temperature decreased by 41°F during the overnight hours.

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Answer: I got you!

Step-by-step explanation:

(a) To find the number of bottles of sanitizer received by each person, we need to divide the total number of bottles by the number of people. So:

Number of bottles per person = (p² + 29p - 96) ÷ (p + 32)

(b) If we substitute x = 8 into the expression for the number of bottles of sanitizer, we get:

p² + 29p - 96 = x(x + 32)

p² + 29p - 96 = 8(8 + 32)

p² + 29p - 96 = 320

p² + 29p - 416 = 0

We can solve this quadratic equation to get:

p = -32 or p = 13

Since the number of people cannot be negative, we take p = 13. Therefore, the actual number of bottles of sanitizer distributed is:

p² + 29p - 96 = 13² + 29(13) - 96 = 520

The number of people who received the sanitizer is:

p + 32 = 13 + 32 = 45

And the share of each person is:

Number of bottles per person = (p² + 29p - 96) ÷ (p + 32) = 520 ÷ 45 ≈ 11.56

So each person received approximately 11.56 bottles of sanitizer.

Answer:

2

Step-by-step explanation:

since d=7 and the equation is d-5 in the place of d we'll put 7 therefore 7-5=2

So, the probability of Freddie getting 4 base hits in a row is approximately 0.0088, or 0.88%.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

by the question.

Assuming that each at-bat is independent of the others, the probability of Freddie getting a base hit in one at-bat is 0.305.

To find the probability that he gets 4 base hits in a row, we can use the multiplication rule for independent events. This rule states that the probability of two or more independent events occurring together is the product of their individual probabilities.

Therefore, the probability of Freddie getting 4 base hits in a row is:

0.305 x 0.305 x 0.305 x 0.305 = 0.0088 (rounded to four decimal places)

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We show that at n = 1 the basis step works, but the inductive step fails.

Let consider the Inequality

[tex]\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}[/tex]

We must demonstrate that while the fundamental step of mathematical induction proves the aforementioned inequality, the inductive step does not.

Mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It involves proving that a statement holds true for a base case (typically zero or one), and then proving that, if it holds true for any given natural number, it must also hold true for the next natural number.

This process is repeated until the statement has been shown to be true for all natural numbers.

Basic Step: n = 1

1/2 < 1/√3, which is true.

Hence we proved that at n = 1  the basic steps of mathematical induction works.

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The complete question is:

Suppose that we want to prove that

[tex]\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}[/tex]

for all positive integers n.

Show that if we try to prove this inequality using mathematical induction, the basis step works, but the inductive step fails.

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. Solving for the radius, we have:

r = C/(2π) = 50.24/(2π) ≈ 8

So the radius of the circle is approximately 8 units.

The formula for the area of a circle is A = πr^2, so we have:

A = π(8)^2 = 64π ≈ 201.06

Therefore, the area of the circle is approximately 201.06 square units.

Answer: 24kg

Step-by-step explanation:

Ratio given:

Dog = 3 (Weight of cat)

Substitute the (Weight of cat) with the given unit:

Dog = 3(8kg)

Multiply

Dog = 24kg

√9+25 = 28

π-4 = -0.8571

³√-27 = -3

2 / 3 = 0.6667

18÷2 = 9

√-27​ = 5.196

In mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).

We have √9+25 = 28

find the square root of 9 = 3

3 + 25 = 28

π-4 = 3.14 - 4

= -0.8571

³√-27 = ³√3³

= 3

2÷3 = 0.6667

18÷2 = 9

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question:

given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27​

find the value of the terms

Continuous variables can take on an infinite number of values whereas discrete variables can only take a value from a finite number of values.

Continuous and discrete variables are two types of variables in statistics. Continuous variables are variables that can take on an infinite number of values, including any fractional value within a particular range.

In contrast, discrete variables can only take on a finite number of values. These values can be counted or enumerated, and there are no fractional values between them.

The distinction between continuous and discrete variables is important in statistical analysis because it affects the methods that can be used to analyze and interpret the data.

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Answer:

the answer

Step-by-step explanation:

61 degrees angle

The features of triangle ABC are:

To check option A, calculate the distance between each pair of points and see if they satisfy the Pythagorean theorem:

AB = \√{(4-3)² + (7-3)²} = \√{41}

BC = \√{(8-4)² + (6-7)²} = \√{17}

AC = \√{(8-3)² + (6-3)²} = 5\√{2}

Now, AB² + BC² = 41 + 17 = AC² is 68 units, which satisfies the Pythagorean theorem and confirms that ABC is a right triangle.

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Answer:

Step-by-step explanation:

First the max degree is 360

Then multiply by 5/8

360 x 5/8 = 1800/8

1800/8 = 225

Answer: 225

The confidence interval suggests that there is no significant difference in CVD risk between smokers and non-smokers, but any potential difference is likely to be small.

The given confidence interval of (-0.01, 0.04) represents a range of plausible values for the difference in the population proportion of CVD between smokers and nonsmokers, with a 95% level of confidence.

A value of 0 suggests no difference in CVD risk between the two groups Since the interval contains both positive and negative values, we cannot conclude with certainty whether the difference is statistically significant or not.

However, the fact that the interval is relatively small suggests that any difference in CVD risk between smokers and nonsmokers is likely to be small in magnitude.

Therefore, the best interpretation of the interval is that there is no strong evidence to suggest a significant difference in the risk, but any potential difference is likely to be small.

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_____The given question is incomplete, the complete question is given below:

In a large study designed to compare the risk of cardiovascular disease (CVD) between smokers and nonsmokers, random samples from each group were selected. The sample proportion of people with CVD was calculated for each group, and a 95 percent confidence interval for the difference (smoker minus nonsmoker) was given as (−0.01, 0.04). Which of the following is the best interpretation of the interval?