Geometric constructions summative- need help on it.... its my end of year project

Part(A),

The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and right endpoints is approximately 0.231 square units.

Part(B),

The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.

To estimate the area under the graph of f(x) = 1/(x²+1) over the interval [3, 5] using four rectangles and right endpoints, we can use the following formula:

[tex]R_n = \dfrac{(b-a)}{n} \times [f(x_1) + f(x_2) + ... + f(x_n)],[/tex]

where a = 3, b = 5, n = 4, and xi = a + i(b-a)/n for i = 0, 1, 2, ..., n.

Using this formula with the right endpoints, we get:

[tex]R_4 = \dfrac{(5-3)}{4 }\times [f(3.5) + f(4) + f(4.5) + f(5)][/tex]

R₄ = (1/2) x [0.361 + 0.250 + 0.178 + 0.132]

R₄ = 0.231

Hence, the estimated area under the f(x) graph utilizing four rectangles and the right endpoints over the range [3, 5] is about 0.231 square units.

To repeat the approximation using left endpoints, we can use the following formula:

[tex]L_n = \dfrac{(b-a)}{n} \times [f(x_0) + f(x_1) + ... + f(x_{n-1)],[/tex]

where [tex]x_i = a + i\dfrac{(b-a)}{n}[/tex] for i = 0, 1, 2, ..., n-1.

Using this formula with left endpoints, we get:

[tex]L_4 = \dfrac{(5-3)}{4} \times [f(3) + f(3.5) + f(4) + f(4.5)][/tex]

L₄ = (1/2) x [0.250 + 0.361 + 0.250 + 0.178]

L₄ = 0.2405

Therefore, the estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.

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For the function f(x) = -2x² + 5x + 7 the slope of the secant line between x = -3 and x = 5 is -4

Consider the function f(x) = -2x² + 5x + 7

We need to find the slope of the secant line between x = -3 and x = 5

We know that the slope of secant line for the function f(x) on the interval [a, b] is given by the formula,

m = [f(b) - f(a)] / (b - a)

Let [a, b] = [-3, 5]

For x = -3 the value of the function would be,

f(-3) = -2(-3)² + 5(-3) + 7

      = -2(9) - 15 + 7

      = -18 - 15 + 7

      = -26

And the value of the function for x = 5 would be,

f(5) = -2(5)² + 5(5) + 7

      = -2(25) - 25 + 7

      = -50 - 15 + 7

      = -58

Using above formula the slope would be,

m = [f(5) - f(-3)] / (5 - (-3))

m = [-58 - (-26)] / 8

m = (-58 + 26) / 8

m = -4

Thus, the required slope is -4

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Answer:

Slope = 1

Step-by-step explanation:

A secant line is a straight line that intersects a curve at two or more points.

Given a curve represented by a function f(x), a secant line is determined by choosing two distinct points on the curve, (x₁, f(x₁)) and (x₂, f(x₂)).

The secant line passes through these two points and can be represented by a linear equation in the form y = mx + b, where m is the slope of the secant line and b is the y-intercept.

The slope of the secant line between the points (x₁, f(x₁)) and (x₂, f(x₂)) is given by the formula:

[tex]m = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

To find the slope of the secant line between x = -3 and x = 5 for the function f(x) = -2x² + 5x + 7, first find f(-3) and f(5).

[tex]\begin{aligned}f(-3)&=-2(-3)^2+5(-3)+7\\&=-2(9)-15+7\\&=-18-15+7\\&=-26\end{aligned}[/tex]

[tex]\begin{aligned}f(5)&=-2(5)^2+5(5)+7\\&=-2(25)+25+7\\&=-50+25+7\\&=-18\end{aligned}[/tex]

Input the values into the slope formula:

[tex]m = \dfrac{f(5) - f(-3)}{5 - (-3)}=\dfrac{-18-(-26)}{5+3}=\dfrac{8}{8}=1[/tex]

Therefore, the slope of the secant line between x = -3 and x = 5 is 1.

Answer:

253 divided by 4 is 63.25.

Here's the work:

```

4) 253.00

   24

  ---

    13

    12

   ---

     13

     12

    ---

      1

```

Therefore, the answer is 63.25.

Answer:

D. It is a two-dimensional object.

The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.

Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.

Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.

Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.

The ROI (Return on Investment) for the above investment is 106.67%.

What is the Return on Investment?

ROI (Return on Investment) is one that is seen as a financial metric used to know the profitability of an investment relative to its cost.

The formula for ROI is:

ROI = (Net Profit / Cost of Investment) x 100%

Hence, the cost of investment is the sum of the price as well as the renovation cost, will be:

Cost of Investment = $100,000 + $50,000

                               = $150,000

Note that the The net profit from the sale of the house is $160,000.

So, the ROI can be calculated as:

ROI = (Net Profit / Cost of Investment) x 100%

= ($160,000 / $150,000) x 100%

= 106.67%

So, the ROI for the above investment is 106.67%.

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Adding the number 6 to the given dataset did not affect the mode, as the number 19 still appeared the most frequently in the new dataset. (option c).

Now, if we add the number 6 to this dataset, we need to determine how this will affect the mode. We can start by looking at the number 19, which was the original mode. If the number 19 still appears the most frequently in the dataset after the addition of the number 6, then the mode will remain 19. However, if another number appears more frequently than 19 after the addition of 6, then the mode will change.

In this case, the number 6 does not appear anywhere in the original dataset, so it cannot be the mode. Therefore, the mode can either remain as 19 or change to a new number, depending on whether any other number appears more frequently than 19 after the addition of 6.

To determine if the mode changes, we need to calculate the frequency of each number in the new dataset. After adding 6, the dataset becomes:

18 24 19

19 18 20

26 25 19

6

From this dataset, we can see that the number 19 still appears twice, while all other numbers appear only once. Therefore, the mode of the new dataset is still 19, and the answer to your question is (C) "The mode will change to one number."

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Complete Question:

What happens to the mode of the data set shown below if the number 6 is added?

18 24 19

19 18 20

26 25 19

A The mode will change to two numbers.

B The mode will increase by 4.

C The mode will change to one number.

D The mode will increase by 2.

A recursive sequence are -20, -80, -320 and  -1280.

To write a recursive sequence that represents the sequence defined by the given explicit formula, we need to find a rule that relates each term of the sequence to the previous term.

The explicit formula for the sequence is

[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]

To find the recursive formula, we need to express each term in terms of the previous term. Let's say the first term of the sequence is  [tex]a_{1[/tex].

[tex]a_{1[/tex]  = -5 * 1 = -5

[tex]a_{2}[/tex] = -5 * 4 = -20

[tex]a_{3}[/tex] = -5 * 16 = -80

...

[tex]a_{n}[/tex] = -5 [tex](4)^{n-1}[/tex]

We can see that each term in the sequence is 4 times the previous term, so we can express the nth term in terms of the (n-1)th term as follows

[tex]a_{1[/tex] = -5

[tex]a_{n}[/tex] =  4[tex]a_{n-1}[/tex] , for n > 1

This gives us the recursive formula for the sequence. To generate the sequence, we start with the initial term [tex]a_{1[/tex] =-5 and use the recursive formula to find the subsequent terms.

For example, if we want to find a5, we can use the recursive formula

[tex]a_{2}[/tex] = 4[tex]a_{1[/tex] = 4(-5) = -20

[tex]a_{3}[/tex] =  4[tex]a_{2}[/tex] = 4(-20) = -80

[tex]a_{4}[/tex] = 4[tex]a_{3}[/tex] = 4(-80) = -320

[tex]a_{5}[/tex] = 4[tex]a_{4}[/tex] = 4(-320) = -1280

Therefore, [tex]a_{5}[/tex] = -1280.

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Answer:

If the diameter of the circle increases to 60 inches, the new area would be approximately 2700 square inches.

If the determinant of the matrix formed by the coordinates of the three points is zero, then they are collinear

Given data ,

To show that three points lie on the same line using coordinate geometry, we need to check if they satisfy the equation of a line.

Let the coordinates of the three points be (x1, y1), (x2, y2), and (x3, y3).

To check if these three points are collinear, we can calculate the slope of the line passing through the first two points using the formula

m = (y2 - y1) / (x2 - x1)

Then, we can check if the slope of the line passing through the second and third points is equal to the slope we calculated above. If they are equal, then all three points lie on the same line

m' = (y3 - y2) / (x3 - x2)

If m = m', then the three points are collinear

Alternatively, we can use the determinant method to check if the three points lie on the same line. If the determinant of the matrix formed by the coordinates of the three points is zero, then they are collinear

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Answer:

Step-by-step explanation:

5 is greater than 0.004

Answer: 5 is greater

Step-by-step explanation:

Maria can estimate the total tuition for all 4 years to be $122400

How to determine the tuition fee?

Tuition payments, usually known as tuition in American English and as tuition fees in Commonwealth English, are fees charged by education institutions for instruction or other services.

The given parameters are

Period of school = a 4-year college

Tuition fee per semester = The tuition is $15,300 per semester.

Number of semester = 2=4 = 8 semesters

Total cost = $15,300 per semester. * 8 = $122400

Therefore the cost of the tuition for 4 years is $122400

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The total amount Maria can estimate for the cost of a 4-year college program at the University of Bayou is $122,400

A college program consists of courses that are taken as part of an accredited course, which leads to the award of a degree.

The tuition per semester for the University of Bayou = $15,300

The number of semester in an academic year = Usually 2 semesters

The number of years Maria intends to spend in college = 4 years

The estimate of the total tuition, found using the basic arithmetic operations is therefore;

Tuition for a 4 year program = 15,300 × 2 × 4 = 122400

The total tuition Maria can estimate for 4 year of college is $122,400

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Answer:

1 and 3 are correct.

1 is correct (supplementary angles)

3 is correct (1 and 3 are vertical angles)

Answer:

Step-by-step explanation:

Distance between 2Points XY=Distance between 2 points YZ=7.615

Distance between 2 points ZX=5.6568

Hence it is an isosceles triangle

Answer:

5

Step-by-step explanation:

300÷2=150 ⇒300 wiggles=10 wiggles⇒ 10÷2=5

Answer:

To find A + B, we need to add the corresponding entries of A and B. That is,

A + B = [a_ij + b_ij],

where a_ij and b_ij are the entries of A and B, respectively, in the ith row and jth column.

Using this formula, we get:

A + B = 7 + (-8) -6 + (-7) 2 + 5

6 + (-1) 6 + (-9) -5 + 4

-5 + 9 -7 + 5 8 + (-4)

= -1 -7 7

5 1

4

Therefore, A + B is the matrix:

-1 -7 7

5 1

4

Answer:

They would have gotten 2 full apples each. There would be 4 left over. If they decided to split those 4 apples, they would have gotten 2 1/2 apples each.

Step-by-step explanation:

20 ÷ 8 = 16 R 4

16 ÷ 8 = 2 (the full apples they got each_)

4 x 2 = 8 (split the 4 apples in half to make 8)

Therefore, each student would have gotten 2 full apples and 1/2 of an apple.

i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0

To use a graph to find the value of x for the given values of y in the equation y=-|x-2|+2, we can follow these steps:

i) When y<0:

The graph of y=-|x-2|+2 is below the x-axis when y<0. Therefore, there is no solution for x when y<0, because there is no point on the graph that has a negative y-coordinate.

ii) When y>0:

The graph of y=-|x-2|+2 intersects the x-axis at two points when y>0. To find the x-coordinates of these points, we can set y=0 in the equation y=-|x-2|+2 and solve for x, as shown in the previous answer.

The x-intercepts are at (4,0) and (0,0), which means that the graph crosses the x-axis at x=4 and x=0 when y>0.

iii) When y=0:

To find the x-coordinate(s) of the point(s) where the graph intersects the x-axis (i.e., where y=0), we can look at the x-intercepts that we found in part ii) above. The x-coordinate(s) of the point(s) where the graph intersects the x-axis are x=4 and x=0, so the solutions for x when y=0 are x=4 and x=0.

Therefore, i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0 (the x-intercepts).

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The real solution is 0, and the imaginary solution is 0.5 ±  0.866i.

The solutions of the equation is calculated as follows;

4x(x² - x + 1) = 0

This equation is satisfied when either 4x = 0 or x² - x + 1 = 0.

If 4x = 0, then x = 0 is a solution,

To find the solutions of x² - x + 1 = 0, we will use formula method;

x = [ -(-1) ± √((-1)² - 4(1)(1)) ] / (2(1))

x = [ 1 ± i√3 ] / 2

x = 0.5 ±  0.866i

Thus, the solutions of the cubic equation involves both real and imaginary solution.

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4) residual =actual -predicted =26708-10376.71 =16331.29

1) predicted change = -140.74

2) predicted change =317.74

3) predicted GNP =-11093.17-140.74*10+317.74*72 =10376.71

4) residual =actual -predicted =26708-10376.71 =16331.29

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

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Answer:

To determine the domain of f - g, we need to first find the expression for f - g.

f - g = (x^2 - 4) - (2x + 3)

f - g = x^2 - 2x - 7

The domain of f - g is the set of all real numbers for which the expression x^2 - 2x - 7 is defined.

We know that a quadratic expression of the form ax^2 + bx + c is defined for all real numbers x, so long as the expression under the square root in the quadratic formula (b^2 - 4ac) is non-negative.

In this case, a = 1, b = -2, and c = -7, so the expression under the square root is:

b^2 - 4ac = (-2)^2 - 4(1)(-7) = 4 + 28 = 32

Since 32 is positive, we know that the expression x^2 - 2x - 7 is defined for all real numbers x, and therefore the domain of f - g is all real numbers.

So the answer is not among the choices given.

0.333 is the probability of choosing a boy.

The probability of boys being selected can be calculated as the ratio of the number of boys to the total number of children:

Probability of selecting a boy = Number of boys / Total number of children

Probability of selecting a boy = 4 / 12 = 1/3

Therefore, the probability of selecting a boy is 1/3 or approximately 0.333.

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Answer:

The expected value in this situation can be calculated as follows:

E(X) = P(X) * V(X), where X is the random variable representing the profit of the construction company, P(X) is the probability of X, and V(X) is the value of X.

In this case, the profit of the construction company if the bid is accepted is $96,000 - $1,100 = $94,900, and the probability of the bid being accepted is 1/10. Therefore, we have:

E(X) = (1/10) * $94,900 = $9,490

The expected value of $9,490 means that in the long run, the construction company would expect to earn this amount on average per bid. Therefore, the correct answer is option A: "In the long run, the construction company would expect to earn this amount on average per bid."

Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.

To calculate the interest Marcus will earn, we can use the formula:

I = P * r * t

where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.

In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.

So we can plug in these values into the formula:

I = 500 * 0.068 * 5

I = $170

This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.

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The explicit formula for the sequence defined by the recursive formula a₁ = 150 and aₙ = -1/5 aₙ₋₁ is aₙ = 150 [tex](-1/5)^{(n-1)[/tex].

To find the explicit formula that represents the sequence defined by the given recursive formula, we need to find a pattern in the sequence and express it using a formula.

The first term in the sequence is a₁ = 150. To find the second term, we use the recursive formula: a₂ = -1/5 a₁ = -1/5(150) = -30. To find the third term, we use the recursive formula again: a₃ = -1/5 a₂ = -1/5(-30) = 6.

We can continue this process to find the fourth term: a₄ = -1/5 a₃ = -1/5(6) = -6/5, and so on.

By observing the pattern, we notice that each term is obtained by multiplying the previous term by -1/5. Therefore, the explicit formula for the sequence can be written as:

aₙ = 150 [tex](-1/5)^{(n-1)[/tex]

This formula gives the value of any term in the sequence based on its position n. It can be used to find any term in the sequence without having to recursively calculate all the previous terms.

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The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' is given as follows:

A rotation followed by a translation.

Examples of transformations are given as follows:

For this problem, we have that the inclination of the figure changed, and the figure moved from the second quadrant to the first/fourth, hence the figure underwent a rotation of 90º counterclockwise about the origin.

The figure also had the vertices changed from the rotation, hence a translation was also applied.

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Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

The mode is the best measure of center for a distribution that is bimodal, meaning that it has two peaks. In such a distribution, the mean and median may not be representative of the center of the data, but the mode is a good measure of center because it reflects the most common value(s) in the data.

For skewed distributions, the mode may not be a good measure of center because the peak of the distribution is not necessarily at the center of the data. In a normal distribution, the mean, median, and mode are all equal and are good measures of center.

Answer:

110

Step-by-step explanation:

nth term = 3n + 2

3 (36) + 2

108 + 2 = 110

Answer:

The 36th term in the sequence is 104.

Here's how to find it:

- Start with the first number in the sequence: 5.

- Add the common difference, which is 3, to get the second number in the sequence: 8.

- Add the common difference to the second number to get the third number: 11.

- Continue adding the common difference to each subsequent number to find the next term in the sequence.

- The 36th term is three less than 37 times the common difference added to the first term.

- Using that formula, we can calculate the 36th term as: 5 + (36 - 1) * 3 = 5 + 105 = 110.

- Therefore, the 36th term in the sequence is 104.

The valid inference based on the information provided is:

Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.

The study involved only 200 volunteers who were already taking blood pressure medication. This is a relatively small sample size and may not be representative of all blood pressure patients. Inferences about all blood pressure patients cannot be made from this limited sample.

While the group taking the new medication showed a significantly lower overall blood pressure than the group taking the original medication, it was also mentioned that the new medication did not significantly lower cholesterol levels.

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From the pharmaceutical company's test, we can conclude that the new medication is more effective than the original in lowering blood pressure for patients already taking blood pressure medication. However, this conclusion doesn't apply to all blood pressure patients.

A valid conclusion from the scenario about the pharmaceutical company's testing of its new medication would be the following: Inferences cannot be made about all blood pressure patients, though the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients who are already taking blood pressure medication. The study has a specific sample population: people who are already taking blood pressure medication. We can't extrapolate this to all blood pressure patients, because the study didn't include those who don't take any medication. However, it was observed that the new medication was more effective in lowering blood pressure than the original one within this specific group.

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Answer:1/4, 25%

Step-by-step explanation:

even number: 2,4,6

odd umber 1,3,5

even number probability when 1 dice is rolled: 3/6 = 1/2

2 dice is rolled: 1/2*1.2 = 1/4 = 25%