Is the data set approximately periodic? If so, what are its period and amplitude?

not periodic

periodic with a period of 4 and an amplitude of about 20

periodic with a period of 4 and an amplitude of about 30

periodic with a period of 5 and an amplitude of about 25

Answer: its 7

Step-by-step explanation:

its 7

By the Triangle Sum Theorem, x + y + a = 180° and x + y + b = 180°. By substitution, x + y + a = 180°. Subtract equal quantities from both sides to get a = b.

In Mathematics, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

x + y + b = 180°

By substitution, we have the following:

x + y + a = 180°

Next, we would subtract equation 1 from equation 2, we have:

a - b = 0

a = b (Prove).

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The middle οf BC and B′C′ shοuld be crοssed by a line. This line serves as the triangle's reflectiοn line.

A line is a straight, οne-dimensiοnal figure in geοmetry that can gο οn fοrever in bοth directiοns. It is frequently depicted as an infinitely lοng straight line with arrοws at bοth ends. Any twο οf its pοints, referred tο as a line's endpοints, are what characterize a line. Geοmetrical cοncepts like angles, planes, and shapes are defined in terms οf lines, which are fundamental geοmetrical οbjects. These can be depicted using mathematical sοftware οr a straightedge and pencil.

Finding the perpendicular bisectοr οf each pair οf related sides is necessary befοre we can cοnstruct the line οf reflectiοn that reflects triangle ABC οntο triangle A′B′C′. We will find the center οf reflectiοn at the pοint where these three perpendicular bisectοrs cοnnect.

Bypassing the intersectiοn οf AB and A′B′, draw a line. Identify this pοint as M.

The middle οf AC and A′C′ shοuld be crοssed by a line. Identify this pοint as N.

The middle οf BC and B′C′ shοuld be crοssed by a line. Identify this pοint as O.

Lοcate where the MN and MO lines cοnverge. Put a P after this place.

The middle οf BC and B′C′ shοuld be crοssed by a line.  This line serves as the triangle's reflectiοn line.

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Complete Question:

Draw the line of reflection that reflects △ABC onto triangle Δ A'B'C'

The arithmetic sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43,....

Common difference = 4

First term = 3

The formula for the sum of the first n terms of an arithmetic sequence is:

Sₙ = ⁿ/₂[2a + (n − 1)d]

where:

n = the number of terms to be added.

a = the first term in the sequence.

d = common difference

We are told that sum of the first 9 term is 171. Thus:

(9/2) [2a + (9 − 1)d]  = 171

(2a + 8d) = 38   ----(1)

Sum of the next 5 term is 235.

Thus, sum of the first 14 terms = 235 + 171 = 406

(14/2) [2a + (14 − 1)d]  = 406

7(2a + 13d) = 406

2a + 13d = 58    -----(2)

Subtract eq 1 from eq 2 to get:

5d = 20

d = 4

2a + 13(4) = 58

2a = 58 - 52

a = 3

Sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43,....

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Answer:

Step-by-step explanation:

h+f

Answer:

The problem seems to be missing some important information such as the scale factor and the coordinates of the points in the original figure. Without this information, I cannot provide a complete solution to the problem. Please provide me with the missing information so I can help you better.

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

'%' literally means 'out of 100'. So if it is 50 out of 100, we can write it as 50/100. This can then be simplified down to 1/2.

Answer:

50% can be written as 50/100 or can be simplified and written as 25/50 or 5/25 or 1/5.

If you want to write it as a whole number, you can divide the fraction of 50% ex:- 1/5. So, the whole number you get is 1/5 = 0.2.

The scientific nοtatiοn fοr 36,000,000 is 3.6 107, where 3.6 is the number between 1 and 10, and 7 is the pοwer οf 10, which gives the number οf digits in 36,000,000.

Scientific nοtatiοn is a way οf representing very large οr very small numbers in a mοre cοmpact and manageable fοrm. It invοlves expressing a number as a prοduct οf a cοefficient and a pοwer οf 10.

Scientific nοtatiοn is a way οf expressing numbers that are very large οr very small using a pοwer οf 10.

The general fοrm οf a number in scientific nοtatiοn is a × 10ⁿ, where a is a number between 1 and 10 (but nοt equal tο 10), and n is an integer.

Hence, The number 36,000,000 can be written in scientific nοtatiοn as 3.6 × 10⁷, where 3.6 is between 1 and 10, and 7 is the pοwer οf 10 that gives the number οf zerοs in 36,000,000.

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Complete Question:

Shantel read that the distance between the sun and Mercury is about 36,000,000 miles. Which of the following correctly represents this distance in scientific notation?

A. 36 x 10⁸

B. 3.6 x 10⁷

C. 3.6 x 10⁻⁷

D. 3.6 x 10⁶

Answer:      from year 3 to 4, percentage is 32%

Step-by-step explanation:       the growth is th largest, showing a difference of eight. and 8% is so little it would not make sense

The proportionality constant, based on the information provided, will be 3/7.

The graph, which is based on the information provided, depicts the relationship between the usage rates of blue and orange fabrics.

As a result, the proportionality constant will be determined as follows:

y = kx

0.085 = 0.2k

k = 0.085/0.2

k = 0.425

k = 3/7

Hence, 3/7 is the right answer.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

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Full Question:

Maya uses blue and orange fabric to make identical wall decorations. The graph below shows the relationship between the amounts of blue and orange fabrics used.

Answer:

28 minutes

Step-by-step explanation:

1/5 × 35 = 7

35 - 7 = 28

(a)the Jordan canonical form of A is:

[tex]\left[\begin{array}{ccc}-1&1&0\\0&3&0\\0&0&3\end{array}\right][/tex]

(b)the Jordan canonical form of A is:

[tex]\left[\begin{array}{ccc}4&0\\0&1\end{array}\right][/tex]

(a) Matrix A = (-1 3)

To find the Jordan canonical form of A, we first need to find the eigenvalues of A. The characteristic polynomial of A is given by:

p(λ) = det(A - λI) = det([-1-λ, 3; 0, 3-λ]) = (λ+1)(λ-3)

So the eigenvalues of A are  λ1= -1 and λ2 = 3.

Next, we need to find a basis for each generalized eigenspace of A. For λ1 = -1, we have:

(A - λ1I) = [tex]\left[\begin{array}{ccc}0&3\\0&4\end{array}\right][/tex]with rank 1

So the dimension of the generalized eigenspace for λ1 is 2 - 1 = 1. We need to find a vector x such that (A - λ1I)x = 0, but (A - λ1I)^2x ≠ 0. In this case, we can take x = (3,0). Then we have:

(A - λ1I)x = [tex]\left[\begin{array}{ccc}1&3\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}3\\0\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0\\0\end{array}\right][/tex]

(A - λ1I)^2x = [tex]\left[\begin{array}{ccc}1&3\\0&4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1&3\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}3\\0\end{array}\right][/tex]= [tex]\left[\begin{array}{ccc}0\\0\end{array}\right][/tex]

So the generalized eigenspace for λ1 is spanned by the vector x = (3,0).

For λ2 = 3, we have:

(A - λ2I) = [tex]\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right][/tex] with rank 1

So the dimension of the generalized eigenspace for λ2 is 2 - 1 = 1. We need to find a vector x such that (A - λ2I)x = 0, but (A - λ2I)^2x ≠ 0. In this case, we can take x = (3,4). Then we have:

(A - λ2I)x = [tex]\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}3\\4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0\\0\end{array}\right][/tex]

(A - λ2I)^2x =[tex]\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}-4&3\\0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}3\\4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0\\0\end{array}\right][/tex]

So the generalized eigenspace for λ2 is spanned by the vector x = (3,4).

Now we can form the Jordan canonical form of A using the basis vectors we found for the generalized eigenspaces:

J = [(c1, 1, 0), (0, λ2, 0), (0, 0, λ2)] = [tex]\left[\begin{array}{ccc}-1&1&0\\0&3&0\\0&0&3\end{array}\right][/tex]

(b) Matrix A = [tex]\left[\begin{array}{ccc}1&2\\3&2\end{array}\right][/tex]

To find the Jordan canonical form of A, we first need to find the eigenvalues of A. The characteristic polynomial of A is given by:

p(λ) = det(A - λI) = det([(1-λ), 2; 3, (2-λ)]) = λ^2 - 3λ - 8 = (λ-4)(λ+1)

So the eigenvalues of A are λ1 = 4 and λ2 = 1.

Next, we need to find a basis for each generalized eigenspace of A. For λ1 = 4, we have:

(A - λ1I) = [tex]\left[\begin{array}{ccc}-3&2\\3&-2\end{array}\right][/tex] with rank 1

For λ2 = 1, we have A - λ2I =

[tex]\left[\begin{array}{ccc}0&2\\3&1\end{array}\right][/tex]

and the corresponding generalized eigenspace is the span of the vectors {(2,-3), (1,0)}. To find a basis for the cycle, we need to find a generalized eigenvector v such that (A - λI)v = (A - I)v = u, where u is the original eigenvector. Solving this equation gives v = (-1,3), so a basis for the cycle is {(2,-3), (1,0), (-1,3)}.

Therefore, the Jordan canonical form of A is:

[tex]\left[\begin{array}{ccc}4&0\\0&1\end{array}\right][/tex]

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For problem (A), subtracting A and B alone cannot solve the problem as the result does not provide the amount of water left in the bowl, and for problem (B), subtracting A and B can solve the problem as it provides the amount of pizza left after James ate.

(A) This problem cannot be solved by subtracting A and B. If we subtract 1/3 from 1/2, we get 1/6, which is the amount of water that was poured out. However, this does not tell us how much water is left in the bowl. To solve the problem, we need to subtract 1/3 from 1/2 and then subtract the result from 1/2. This gives us

1/2 - 1/3 = 1/6

1/2 - 1/6 = 1/3

Therefore, there is 1/3 cup of water left in the bowl.

(B) This problem can be solved by subtracting A and B. If James ate 1/2 of the pizza yesterday and 1/3 of the pizza today, then he ate a total of

1/2 + 1/3 = 5/6

of the pizza. Therefore, the amount of pizza left is:

1 - 5/6 = 1/

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The given question is incomplete, the complete question is:

determine whether the problem can be solved by subtracting A and B . If not, explain why not, and explain how the problem should be solved if there is enough information to do so

A) Zelha pours 1 2 cup of water into an empty bowl and then pours out 1 3. How much water is in the bowl now? Zelha pours 1 2 cup of water into an empty bowl and then pours out 1 3 cup of water. How much water is in the bowl now? (B)  Yesterday James ate 1 2 of a pizza, and today he ate 1 3 of the whole pizza. Nobody else ate any of that pizza. How much pizza is left?

Answer:

360 adult tickets and 800 student tickets were sold.

Step-by-step explanation:

Let's use a system of equations to solve this problem.

Let x be the number of adult tickets sold, and y be the number of student tickets sold. We know that a total of 1,160 tickets were sold, so:

x + y = 1160

We also know that the total amount collected was $2,600. The amount collected from adult tickets is $5 times the number of adult tickets sold, and the amount collected from student tickets is $1 times the number of student tickets sold. So:

5x + 1y = 2600

Now we have a system of two equations:

x + y = 1160

5x + y = 2600

We can solve for one of the variables in terms of the other, and substitute into the other equation to solve for the remaining variable. For example, we can solve the first equation for y:

y = 1160 - x

Now substitute this expression for y into the second equation:

5x + (1160 - x) = 2600

Simplifying and solving for x:

4x + 1160 = 2600

4x = 1440

x = 360

So 360 adult tickets were sold. To find the number of student tickets sold, we can use either equation. Let's use the first equation:

x + y = 1160

360 + y = 1160

y = 800

So 800 student tickets were sold.

Therefore, 360 adult tickets and 800 student tickets were sold.

The center of the circle is (7, -4). The new center of the new circle is (9, 0). The new equation of the circle is:

(x + 9)² + y² = 6²

Given the circle's center and radius, the equation of a circle offers an algebraic approach to describe a circle. The formulae used to determine a circle's area or circumference are different from the equation for a circle. Many coordinate geometry problems involving circles employ this equation. We need the equation of the circle in order to represent a circle on the Cartesian plane. If we are aware of a circle's centre and radius, we can draw it on a sheet of paper. Similar to this, if we know the coordinates of the center and radius of a circle on a Cartesian plane, we can draw it.

The general equation of the circle is given as:

(x - h)² + (y - k)² = r²

Where, h and k are the coordinates of the center.

The given equation is (x + 7)² + (y - 4)² = 6²

The center is (7, -4).

Given that, the circle is shifted by 3 units to the right and 4 down.

Then the x-coordinate of the circle is:

x + (7 + 3) = (x + 9)

and y-coordinate is:

y - (4 - 4) = y

Thus, the new equation of the circle is:

(x + 9)² + y² = 6²

The new center of the new circle is (9, 0).

Hence, the center of the circle is (7, -4). The new center of the new circle is (9, 0). The new equation of the circle is:

(x + 9)² + y² = 6²

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Answer:

.8/10

Because Lisa made 80 out of 100 free throws, and her probability of making a free throw is 0.8, the probability would be .8/10.

Step-by-step explanation: this may be wrong due to lack of detail in the question.

there are four numbers in this data set we divide by 4 to get the mean which is 6.5/4 = 1.6251.

What  is mean ?

The mean is generally the average of a given set of numbers. It is the value that gives the central tendency from a given set of observations.

In statistics, three measures define the central values of the observed data they are mean, median, and mode

The mean for a given set of numbers can be computed in more than one way, including the arithmetic mean method, which uses the sum of the numbers in the series

The mean of a data set is calculated by adding up all the numbers in the data set and then dividing by the total number of values in the set.

In this case, we have a data set of

{1/2,1/3,2/3,11/2}.

Adding these numbers together gives us

1/2 + 1/3 + 2/3 + 11/2 = 6.5.

Since there are four numbers in this data set,

we divide by 4 to get the mean which is 6.5/4 = 1.6251.

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We reject the null hypothesis that a sample of 400 observations with mean 95 and standard deviation 12 was randomly drawn from a population with mean 98 at a 5% level of significance.

To test whether a sample of 400 observations has been randomly drawn from a population with a mean of 98, we can use a one-sample t-test. The null hypothesis for this test is that the sample was drawn from a population with a mean of 98, while the alternative hypothesis is that the sample was not drawn from a population with a mean of 98

To perform the t-test, we can first calculate the t-statistic

t = (X - μ) / (s / sqrt(n))

where X is the sample mean, μ is the population mean (which is given as 98), s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get

t = (95 - 98) / (12 / sqrt(400)) = -5

The degrees of freedom for this test are (n - 1) = 399. Using a t-table with 399 degrees of freedom and a significance level of 0.05, we find that the critical t-value is -1.965 (assuming a two-tailed test).

Since our calculated t-value of -5 is less than the critical t-value of -1.965, we can reject the null hypothesis and conclude that the sample was not drawn from a population with a mean of 98 at a significance level of 0.05. Therefore, we can conclude that the mean of the population from which the sample was drawn is unlikely to be 98.

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256 in²  is the area of the triangle represented.

What is known as a triangle?

A triangle is a three-sided polygon because it has three vertices. The connection of the three sides end to end at a single point creates the angles of the triangle.

                                 The triangle's three points amount to a sum of 180 degrees. This two-dimensional shape has three straight sides. A triangle is included as a polygon with three sides. The sum of the three angles in a triangle is 180 degrees.

Area of a triangle = 1/2 * base * height

for this triangle:       base = 32 in       height = 16 in

 area = 1/2 ( 32)(16)  = 256 in²

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The final form of the exponential function is: f(t) = 750(0.8825)raise to the power t

what is exponential function?

An exponential function is a mathematical function of the form f(x) = a to the power x, where "a" is a positive constant (called the base of the exponential function) and "x" is a variable that can take on any real number value.

The key property of an exponential function is that the output value (or "y" value) grows or decays at a constant rate as the input value (or "x" value) increases or decreases. This constant rate of growth or decay is determined by the base "a" of the function.

When the base "a" is greater than 1, the function represents exponential growth, where the output value increases rapidly as the input value increases. When the base "a" is between 0 and 1, the function represents exponential decay, where the output value decreases rapidly as the input value increases.

Exponential functions are commonly used to model natural phenomena such as population growth, radioactive decay, and compound interest. They also have many applications in science, engineering, economics, and finance.

Starting with the given exponential function:

f(t) = 750(0.65)raise to the power (t/35)

We can rewrite 0.65 as 0.65, and 35 as 5 * 7. Then we have:

f(t) = 750(0.65)raise to the power (t/(5*7))

Using the exponent rule that (a to the power b)to the power c = a to the power (bc), we can simplify the expression inside the parentheses:

f(t) = 750(0.65 to the power (t/5))⁷

Letting a = 750 and b = 0.65 to the  power(1/5), we can write the function in the desired form:

f(t) = ab to the power , where a ≈ 750 and b ≈ 0.8825 (rounded to four decimal places)

Therefore, the final form of the exponential function is:

f(t) = 750(0.8825) to the power t

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The answer is that the z score is unusual. We can calculate it in the following manner.

To calculate the z-score for a score of 72, we can use the formula:

z = (x - μ) / σ

where x is the individual score, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (72 - 77) / 2 = -2.5

Rounding to two decimal places, the z-score is -2.50.

To determine if this z-score is unusual, we need to compare it to a standard normal distribution. In a standard normal distribution, about 95% of the data falls within 2 standard deviations of the mean (i.e., between a z-score of -2 and +2). A z-score beyond this range is generally considered unusual.

Since the z-score for a score of 72 is beyond this range (i.e., it is less than -2), it is considered unusual.

Therefore, the answer is:

Unusual

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a) $250

b) C(x) =$200 + x*$50

c) The graph is in the image at the end.

d) The equation is not proportional.

There is a fixed charge of $200 and $50 per month, so the cost after 1 month will be:

C(1) = $200 + $50 = $250

b) Now we want to get the cost after x months, it will be $200 plus x times the $50 charged per month, then we will get:

C(x) =$200 + x*$50

That linear equation models the cost.

c) To graph this, evaluate the line in two different values of x, then graph the obtained points, and connect them with a line.

c(0) = $200 + 0*$50 = $200

So we have the points (0, 200) and (1, 250), with these two we can get the graph of the line you can see at the end.

d) No, the relation is not proportional because there is a fixed value of $200.

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The process capability index for this lab is 5.14

We know that the formula for the process capability index is:

[tex]C_{p}=min(\frac{X-LS}{3\sigma} , \frac{US-X}{3\sigma} )[/tex]

Here, the average turnaround(X) = 26.2

the standard deviation ( σ) = 1.05 minutes

the nominal value for service = 30 minutes

the upper specification= 50 minutes

and lower specification = 10 minutes

Using above formula the  process capability index would be,

[tex]C_{p}=min(\frac{X-LS}{3\sigma} , \frac{US-X}{3\sigma} )\\\\C_{p}=min(\frac{26.2-10}{3\times 1.05} , \frac{50-26.2}{3.15} )\\\\C_{p}=min(\frac{16.2}{3.15} , \frac{23.8}{3.15} )\\\\C_{p}=min(5.14, 7.56)\\\\C_{p}=5.14[/tex]

Therefore, the  process capability index is 5.14

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If we roll two die, number of possible outcome is 1 and total number of outcome is 36 therefore the the probability of rolling a one on the first die and a three on the second die is 1/36.

Total number outcome is :

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Number of possible outcome is 1

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The function to represent the average cost of each satellite television subscription per month would be:

f(x) = (140 + 30x) / 60 for the Orbit company

f(x) = (20 + 35x) / 60 for the Vision company

What is time complexity?

Time complexity refers to the amount of time an algorithm or program takes to run as the input size increases. It is a measure of the efficiency of an algorithm, and it is usually expressed in terms of the "big O" notation.

Cost of Orbit company subscription

= $140 + ($30/month * 12 months * 5 years) = $2140

Cost of Vision company subscription

= $20 + ($35/month * 12 months * 5 years) = $2120

Therefore, the average cost of each satellite television subscription per month for the given period is:

(Cost of Orbit subscription + Cost of Vision subscription) / (12 months * 5 years) = ($2140 + $2120) / (12 * 5) = $35.67 per month

Time complexity O(1), and space complexity V(1) because the calculation only involves basic arithmetic operations and a fixed number of variables.

So, the function to represent the average cost of each satellite television subscription per month would be:

f(x) = (140 + 30x) / 60 for the Orbit company

f(x) = (20 + 35x) / 60 for the Vision company

where x represents the number of years Federico plans to stay in his house.

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Answer:

If the area of a circle is 2.0096 square miles. The circle's radius is 0.8 .

Answer:

b) [tex]\sqrt{208}[/tex]

Step-by-step explanation:

The distance from B to D splits the rectangle into two right triangles with the same dimensions. This distance also equals the hypotenuse of either triangle so pick one triangle to work off of. I will work with triangle BCD.

To solve this problem, you must use the Pythagorean Theorem:

[tex]a^{2} + b^{2} = c^{2}[/tex]

where "a" is one leg of the triangle, "b" is the other leg, and "c" is the hypotenuse.

Leg BC = 8 meters and leg DC = 12 meters.

Substitute "a" as leg BC so [tex]a = 8[/tex].

Substitute "b" as leg DC so [tex]b = 12[/tex]

Now we just plug in our values to find "c", the hypotenuse.

[tex]a^{2} + b^{2} = c^{2} \\8^{2} + 12^{2} = c^{2}\\64 + 144 = c^{2}\\208 = c^{2}\\c = \sqrt{208}[/tex]

Therefore, the answer is b) [tex]\sqrt{208}[/tex]

In an inverse variation  as one value increases, the other decreases. Option D

Inverse variation is a mathematical relationship between two variables in which the product of the two variables is a constant. In other words, if the value of one variable increases, then the value of the other variable decreases in such a way that their product remains constant.

For example, if y is inversely proportional to x, then we can write it as y = k/x, where k is the constant of variation. As x increases, y must decrease to keep the product of x and y constant.

So, the correct answer is D, as one value increases, the other decreases. As one value decreases, the other increases to maintain the constant product. Inverse variation is also called inverse proportionality.

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If the hοtel rοοm fοr Karina and her friend cοsts $86 and they park fοr 7 hοurs, then she will pay $119.

The cοst οf anything is the sum οf mοney οr resοurces that must be used up in οrder tο acquire οr manufacture it. It is a measurement οf the cοsts incurred tο attain a specific οbjective οr result.

The expressiοn tο represent the cοst οf Karina's theme park trip wοuld be:

38 + 10 + 4h + (1/2)r

This includes the $38 entry price, the $10 lunch expense, and the $4 per hοur parking expense fοr the 72 hοurs. Given that Karina and her friend are splitting the cοst οf the hοtel rοοm, the final phrase (1/2)r denοtes Karina's pοrtiοn οf the expense.

If the hοtel rοοm fοr Karina and her friend cοsts $86 and they park fοr 7 hοurs, we can change these values intο the fοrmula tο make it simpler:

= 38 + 10 + 4(7) + (1/2)(86)

= 38 + 10 + 28 + 43

= $119

Therefοre, Karina will pay $119 fοr her theme park trip.

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The probability that fewer than two of the seven households are one-person households is:P(x ≤ 1) = P(0) + P(1) = 0.002 + 0.0322 = 0.0342.

The statistical abstract of the United States reports that 38 percent of the country's households are composed of one person. If 7 randomly selected homes are to participate in a Nielsen survey to determine television ratings, the probability that fewer than two of these homes are one-person households is 0.0813.Explanation:Given that the statistical abstract of the United States reports that 38% of the country's households are composed of one person.Now, we have to find the probability that fewer than two of these homes are one-person households when 7 randomly selected homes participate in a Nielsen survey to determine television ratings.

We are given: The proportion of one-person households = 38% = 0.38. The proportion of households with more than one person = 100% - 38% = 62% = 0.62. We are supposed to find the probability that fewer than two of the seven households are one-person households.The required probability is the sum of the probabilities of selecting 0 one-person households and 1 one-person household.

P(x ≤ 1) = P(0) + P(1)P(0) = probability of selecting 0 one-person households P(1) = probability of selecting 1 one-person householdn = 7, r = 0 P(0) = (7C0)(0.38)^0(0.62)^(7-0) = 0.002 P(1) = (7C1)(0.38)^1(0.62)^(7-1) = 0.0322

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