Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed. 50 Points!!

The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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Answer:

You will pay $457.56.

Step-by-step explanation:

600 x .18 = 108  This is the amount taken off

600 - 108 = 492 Now we will take 7% off of 492

492 x .07 = 34.44

492 - 34.44 = 457.56

The percentage of Measurements that are 124.4 or higher is approximately 0.99%.

In order to determine the percentage of measurements that are 124.4 or higher in a population of measurements that is approximately normal with a mean of 95 and a standard deviation of 15, we need to use the z-score formula.

The z-score formula is used to standardize a distribution so that it can be compared to a normal distribution with a mean of 0 and a standard deviation of 1.

The formula for calculating the z-score is: z = (x - μ) / σWhere:x is the measurement we want to standardize.μ is the population mean.σ is the population standard deviation.

The first step is to calculate the z-score for the measurement of 124.4:z = (124.4 - 95) / 15z = 2.2933The second step is to find the percentage of measurements that are 124.4 or higher using a standard normal distribution table. We look up the area to the right of the z-score of 2.2933 in the table.

The closest value in the table is 0.9901, which corresponds to a z-score of 2.33. We know that the area to the left of a z-score of 2.33 is 0.9901, so the area to the right of a z-score of 2.33 is:1 - 0.9901 = 0.0099

This means that approximately 0.99% of the measurements are 124.4 or higher.

Therefore, the percentage of measurements that are 124.4 or higher is approximately 0.99%.

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The equation for the asymptote of the graphed function is x = 7

The asymptote is a endlessly tendency to a given value. A vertical one is a tendency to infinity.

Here we can see that there is a vertical asymoptote, notice that in one end the function tends to positive infinity and in the other it tends to negative infinity.

The equation of the line where the asymptote is, is:

x = 7

So that is the answer.

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Answer:

The length of the base will be: 17 m

Step-by-step explanation:

Given the area of the triangle

\(A=102\:m^2\)

Using the formula of Area of a triangle:

\(A=\frac{1}{2}\left(b\times h\right)\)

Here,

As the base of a triangle is 7 less than twice its height.

so

\(b=2h-7\)

so the formula of Area of a triangle becomes

\(102=\frac{1}{2}\left(\left(2h-7\right)\times \:h\right)\)

\(204=h\left(2h-7\right)\)

\(2h^2-7h=204\)

\(2h^2-7h-204=0\)

\(\left(2h+17\right)\left(h-12\right)=0\)

\(2h+17=0\quad \mathrm{or}\quad \:h-12=0\)

\(h=-\frac{17}{2},\:h=12\)

As height can not be negative, so:

\(h=12\) m

Hence, the length of the base:

\(b=2h-7\)

   \(= 2(12)-7\)

    \(=24-7\)

     \(= 17\) m

Therefore, the length of the base will be: 17 m

The true statements for all invertible n×n matrices A and B are:

C. \((In+A)(In+A^{-1})=2In+A+A^{-1}\)

D. \(A^6\) is invertible.

To find the true statement, check all options as follows:

\(A. (A+B)^{2}=A^{2}+B^{2}+2AB:\)

This statement is not necessarily true for all invertible matrices A and B. Matrix multiplication is not commutative, so the order matters. Therefore, the expression \((A+B)^2\) is not generally equal to \(A^2 + B^2 + 2AB\).

B. \(A+A^{-1}\) is invertible:

This statement is unless A is a symmetric matrix. For example, if

\(A=\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\)

Then,

\(A=\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\)

So that A+A-1 is a zero matrix that is not invertible.

C. \((In+A)(In+A^{-1})=2In+A+A^{-1}\):

This statement is true. It is a direct consequence of the properties of the identity matrix and matrix multiplication.

\((In + A)(In + A^{-1}) = In(In + A^{-1}) + A(In + A^{-1})\\ = In + A^{-1} + A + AA^{-1}\\ = 2In + A + A^{-1}\)

D. \(A^6\) is invertible:

This statement is not necessarily true.

The invertibility  \(A^6\) depends on the specific matrix A.

In general, raising an invertible matrix A to a power does not guarantee the invertibility of the resulting matrix.

E. \((A+A^{-1})^{9}=A^{9}+A^{-9}\):

This statement is not necessarily true. Again, the order of matrix multiplication matters, and the powers of A and \(A^{-1}\)do not commute. Therefore, \((A + A^{-1})^9\) is not generally equal to \(A^9 + A^{-9}\).

F. AB=BA:

This statement is false.

In general AB ≠ BA as matrix multiplication is not commutative.

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The complete question is as follows:

Select all statements below which are true for all invertible n×n matrices A and B.

\(A. (A+B)^{2}=A^{2}+B^{2}+2AB\\B. A+A^{-1}\ is\ invertible\\C. (In+A)(In+A^{-1})=2In+A+A^{-1}\\D. A^6\ is\ invertible\\E. (A+A^{-1})^{9}=A^{9}+A^{-9}\\F. AB=BA\)

Answer:

its A

Step-by-step explanation:

Answer:

the answer us obtuse triangle.

Answer:

ok look at comments for answers

Step-by-step explanation:

Answer:

24. -3, -1, 0, +1, +3

25. -4, -3, -2, +1, +2

26. -1, 0, +5, +7, +8

27. -7, -4, 0, +2, +3

28. -3, -2, -1, +4, +6

29. -11, -7, -4, +1, +3

:)

The population of the country in 2001 to the nearest hundredth of a million is 24.31 million

If the population grows by 6.5% every year, the population grows at a compound rate. The equation that can be used to determine the population in 2001 would be an exponential equation. The equation that can be used to represent an exponential equation is: a = \(mx^{b}\)

When a population grows at a compound rate, it means that both the existing population and the increase in the population increase by 6.5 every year.

The equation that can be used to determine the population of Tacoma in 2017 is:

P =  FV / (1 + r)^n

Where:

33.3 / ( 1 + 0.065)^5

33.3 / (1.065^5) = 24.30503 million

In order to round 24.30503 million to the nearest hundredth , look at the thousandth figure, if it is greater or equal to 5, add one to the hundredth digit and change the thousandth digit to 0. So,  24.30503 million becomes  24.31 million

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Answer:

10 more than the product of 3 and x

= 3x + 10

9 less than the quotient of n and 5

= n/5 - 9 (n divided by 5 minus nine)

8 times the product of 5 and t

= 8 x 5t

3 times the sum of x and 5

= 3 x (x + 5)

$6.00 entry fee plus $7.50/night of camping

= 6 + 7.5n

Answer:

Step-by-step explanation:

Answer:

your answer will be option D) all real numbers

Step-by-step explanation:

have a nice day/night !! ^_^

Answer:

b= -9

Step-by-step explanation:

Plug in -9 for b.

3= -9+12

Solve.

3=3

Since both sides are equal, the answer is -9

I hope this helped you ;)

The given sequence is 9, 16, 24, 33. To find the next number, let's look for a pattern in the differences between the terms.

The difference between 16 and 9 is 7, between 24 and 16 is 8, and between 33 and 24 is 9.

The pattern in the differences is that they are increasing by 1 each time. So, the next difference would be 10.

To find the next number, we add the next difference to the last term in the sequence. Adding 10 to 33 gives us 43.

Therefore, the next number in the sequence is 43.

To find the next number in the given sequence, we looked for a pattern in the differences between the terms. We observed that the differences were increasing by 1 each time. Using this pattern, we added the next difference to the last term in the sequence to find the next number.

The next number in the sequence 9, 16, 24, 33 is 43.

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A histogram is a chart that is used to display the distribution of a set of data. A histogram is useful because it enables you to visualize how data is distributed in a clear and concise manner. A histogram is a type of bar graph that displays the frequency of data in different intervals.

It is used to show the shape of distribution, presence of outliers, modality, quartile values, and other important information about the data. The following are the different types of things a histogram can help us visualize:a. Shape of distribution (normal, right-skewed, left-skewed): A histogram can help us visualize the shape of distribution of data. The shape of the distribution can be normal, right-skewed, or left-skewed.b. Presence of outliers: A histogram can help us visualize the presence of outliers in data.

An outlier is a value that is significantly different from other values in the data set.c. Modality (unimodal, bimodal, multi-modal): A histogram can help us visualize the modality of data. The modality refers to the number of peaks or modes in the data set. Data can be unimodal, bimodal, or multi-modal.d. Quartiles Values (1st quartile, 2nd quartile or median, 3rd quartile): A histogram can help us visualize the quartile values of data. The quartiles divide the data set into four equal parts, and they are used to describe the spread of data. The first quartile is the value below which 25% of the data falls, the second quartile is the median, and the third quartile is the value below which 75% of the data falls.

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Answer:

6y

Step-by-step explanation:

3(2y)

= 6y

So, the answer is 6y

Answer:

The answer is C

Step-by-step explanation:

2x10=20

2+10=12

20-12=8

10 is 8 more than 2

For a process to be considered in control, the output sample means should be within the control limits and ideally, the distribution of the means should be normally distributed.

However, the process can still be considered in control if the means are uniformly distributed or increasing over time, as long as they are within the control limits. The key is consistency and stability, and if the means are consistently within the control limits, it indicates that the process is predictable and reliable.

Therefore, options (b) and (d), which suggest that the output is increasing or decreasing over time, respectively, are incorrect.

Option (c), which suggests that the output is normally distributed, is not necessarily required for a process to be considered in control. The distribution of the output may vary depending on the process, and as long as the output is within the control limits and stable over time, it can be considered in control.

Option (a), which suggests that the output is uniformly distributed, is not a requirement for a process to be considered in control.

Option (e), which suggests that the output is uniformly distributed and increasing over time, is not a valid option. The output cannot be uniformly distributed and increasing over time at the same time.

Thus, for a process to be considered in control, the output sample means should be within the control limits and ideally, the distribution of the means should be normally distributed.

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Answer:

Step-by-step explanation:

The approximate probability that one of the 1000 books published this week will contain almost 3 pages with errors is 0.414 or 41.4%. Note that this is an approximation because the Poisson distribution assumes independence between the trials, but errors may be correlated within a book or across books.

To solve this problem, we can use the Poisson distribution, which approximates the probability of rare events occurring over a large number of trials. In this case, the rare event is a page containing an error, and the large number of trials is the 1000 books published.
The average number of pages with errors per book is p * number of pages = 0.005 * 500 = 2.5. Using the Poisson distribution, we can find the probability of having almost 3 pages with errors in one book:
P(X = 3) = (e^(-2.5) * 2.5^3) / 3! = 0.143
This is the probability of having exactly 3 pages with errors. To find the probability of having almost 3 pages (i.e., 2 or 3 pages), we can sum the probabilities of having 2 and 3 pages:
P(X = 2) = (e^(-2.5) * 2.5^2) / 2! = 0.271
P(almost 3 pages) = P(X = 2) + P(X = 3) = 0.271 + 0.143 = 0.414
Therefore, the approximate probability that one of the 1000 books published this week will contain almost 3 pages with errors is 0.414 or 41.4%. Note that this is an approximation because the Poisson distribution assumes independence between the trials, but errors may be correlated within a book or across books.

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Displacement from the origin will be 16.76 block

Pythagoras Theorem:

                                   Pythagoras theorem can be used to find the unknown side of a right-angled triangle.Theorem stats that,

                c² = a² + b²

                         where 'c' is the hypotenuse and 'a' and 'b' are the two legs.

In figure,

              O is origin,

             First travel 21 block north that means OA = 21 block.

             then,

                         travel 16 block East that means AB = 16 block.

             again finally,

                        travel 26 block South that means BC = 26 block.

Join OC,

            OC = 16 block

            CD = 5 block

we have to find the value of OD

Apply Pythagoras theorem,

                                                OD² = OC² + CD²

                                                OD = √(OC² + CD²)

                                                OD =√(16² + 5²)

                                                OD =√(256 + 25)

                                                 OD = √(256 + 25)

                                                 OD = √281 block

                                                 OD = 16.76 block

Thus,

              Displacement from the origin will be 16.76 block

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Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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The value of y in the triangle is 20°

Consider the labeling on the image I attached

Since vertically opposite angles are equal. Thus:

x = 50°

Since the sum of angles on a straight line is 180°. Thus:

t + 70° = 180°

t = 180°-70°

t = 110°

Since the sum of angles in a triangle is 180°. Thus:

x + t + y =  180°

50 + 110 + y =  180°

160 + y = 180

y = 180 - 160

y = 20°

Therefore, the value of y is 20°

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What is the percent​ increase from $200 to $280?

There was 40% increase from $200 to $280

What would be the percent increase if the airline charges an additional​ $50 baggage fee with the new ticket​ price?

There was 65% increase with the baggage fee.

#1

Rate of increase (Percent increase)

\(\\ \tt\hookrightarrow \dfrac{80}{200}\times 100\)

\(\\ \tt\hookrightarrow 40\%\)

#2

Percent increase:-

\(\\ \tt\hookrightarrow \dfrac{130}{200}(100)\)

\(\\ \tt\hookrightarrow 65\%\)

The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

In the question ,

it is given that ,

the initial point of the vector = (1 , -1)

the terminal point of the vector = (4,2)

we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

V = (x₂ - x₁)i + (y₂ - y₁)j

Substituting the values from the point ,

we get the vector as

V = (4 - 1)i + (2 -(-1))j

V = 3i + (2 + 1)j

V = 3i + 3j

Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

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Answer:

P(A) = 4/7.

Step-by-step explanation:

Probability it does not occur = 3/7 so probability it does is 1 - 3/7.

P(A) = 1 - 3/7 = 4/7.

The SRS of 125 students is more likely to produce a sample result closer to the true population value.

An SRS (Simple Random Sample) of 125 students allows for a larger sample size, which provides more accurate results.

A larger sample size reduces the effects of random errors and increases the accuracy of the results.

This is due to the fact that the larger the sample size, the more likely it is to be representative of the population.

Additionally, a larger sample size increases the reliability of the results, as it increases the power of the test. Finally, a larger sample size allows for more data to be collected and analyzed, which can provide a clearer picture of the true population value.

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Answer:

Graph will shift 2 units to the left