Find the 16th term of the sequence.217 = -5, d = - 15

Answer:

(a) 19.63 ft

(b) 147.26 ft^2

Step-by-step explanation:

(a) 75/360 degrees . 2 . pi . 15 = 19.63

(b) 75/360 degrees. pi . 15^2 = 147.26

Answer:

a) 19.63 ft (2 dp)

b) 147.26 ft² (2 dp)

Step-by-step explanation:

To find the length of the curved fence, use the formula for arc length of a circle.

To find the area of the vegetable garden, use the formula for area of a sector of a circle.

Formula

\(\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)\)

\(\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2\)

\(\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}\)

Calculation

Given:

\(\begin{aligned}\implies \textsf{Arc length} &=2 \pi (15)\left(\dfrac{75^{\circ}}{360^{\circ}}\right)\\ & = 30 \pi \left(\dfrac{5}{24}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf ft\:(2\:dp)\end{aligned}\)

\(\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{75^{\circ}}{360^{\circ}}\right) \pi (15)^2\\& = \left(\dfrac{5}{24}\right)\pi \cdot 225\\& = \dfrac{375}{8} \pi\\& = 147.26\: \sf ft^2 \:(2\:dp)\end{aligned}\)

The given differential equation is not exact. To check if the differential equation is exact, we need to take partial derivatives of each term with respect to x and y and check if they are equal.

Since the partial derivatives are not equal, the differential equation is not exact.

To solve this equation, we need to use an integrating factor, a function that multiplies the entire equation to make it exact. The integrating factor for this equation is e^x:

Multiplying both sides of the equation by e^x, we get:

Now, if we take partial derivatives of each term with respect to x and y, we find that they are equal:

Since the partial derivatives are equal, the differential equation is now exact.

To solve the equation, we can integrate each term with respect to its corresponding variable. The solution is given by:

where C is the constant of integration.

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Answer:

A plastic board

Answer: b. Simon should chose option a. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options.

Statement B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options is correct.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The probability that the sum of the rolls is a prime number:

P(sum is prime) = 15/36 =0.416

Expected number of points = 0.416×15 =6.25

Probability that f the sum of the rolls is a multiple of 3,

P(sum of rolls is multiple of 3) = 12/36 = 0.33

Expected number of points = 0.33×12 = 3.96

Thus, statement B. Simon should choose Option A. The mathematical expectation of this option is 6.25 and is the greater mathematical expectation of the two options is correct.

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Answer:

C. 2x^4; E. -5x

Step-by-step explanation:

P(x) = x^3 − x − 2 and Q(x) = x^2 + 2x + 1

P(x) * Q(x) = (x^3 − x − 2)(x^2 + 2x + 1) =

= x^5 + 2x^4 + x^3 - x^3 - 2x^2 - x - 2x^2 - 4x - 2

= x^5 + 2x^4 - 4x^2 - 5x - 2

Answer: C. 2x^4; E. -5x

This is an example of a c)confounding variable. A confounding variable is a type of bias that occurs when the researcher is unable to accurately determine the cause of the results.

In this case, the researchers cannot tell if the difference in yield between soybean type 1 and soybean type 2 is a result of the superiority of type 1 soybeans or the drought, so the drought is the confounding variable.

To accurately determine the cause of the difference in yield, a bias-matched pairs design should be used. This involves replicating the experiment by planting both soybean types in the same location with and without the drought, and then comparing the results.

This would reveal whether the difference in yield was actually caused by the superiority of type 1 soybeans or the drought.

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Answer:

confounding variable

Step-by-step explanation:

I got it right on the test :)

Answer:

\(a_2=6\)

Step-by-step explanation:

Geometric sequence general formula:  \(a_n=ar^{n-1}\)

Given:

Therefore,

\(a_1=2 \implies a=2\)

\(a_3=2 \cdot r^2=18\)

\(a_5=2 \cdot r^4=162\)

To find common ratio r, divide 5th and 3rd terms:

\(\dfrac{a_5}{a_3}=\dfrac{2 \cdot r^4}{2 \cdot r^2}=\dfrac{162}{18}\)

\(\implies r^2=9\)

\(\implies r=\sqrt{9}=3\)

Therefore, geometric sequence formula:  \(a_n=2 \cdot 9^{n-1}\)

So second term of sequence:

\(\implies a_2=2 \cdot 3^{2-1}=6\)

Answer:

82 is the median

Step-by-step explanation:

Answer:

The total cost for the three buildings was $6,034,250.

Step-by-step explanation:

Given,

The first sold for $1,259,300,

the second sold for $2,839,750,

the third sold for $1,935,200.

We add these three sold cost of apartment buildings

$1,259,300 + $2,839,750 +  $1,935,200 = $6,034,250.

To calculate the total cost of three things, you will need to add the individual costs of each item together.

1. Determine the cost of each item. Add together the cost of all three items. This total is the cost of the three items.

2. If the items are sold as a package, determine the cost of the package. This is the cost of the three items.

3. If the items are sold at a discounted rate, calculate the total cost of each item after the discount has been applied. Add together the costs of the three items after the discount has been applied. This total is the cost of the three items.

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Answer:

81

Step-by-step explanation:

Using the rule of exponents/ radicals

\(a^{\frac{m}{n} }\) = \((\sqrt[n]{a} )^m\) then

\(27^{\frac{4}{3} }\)

= \((\sqrt[3]{27} )^4\)

= \((3)^{4}\)

= 81

Answer:

here down is the answer

(2y/5y)^3+4y^2+6y

8y^3/125y^3 +16y^2+6y

8/125+16y^2+6y

8/125+16y^2+6y=0

16y^2+6y+8/125=0

it is in the form of quadratic equation

formula :

x=(-b+-square root of b^2-4ac) /2a

here a=16,b=6&c=8/125

x=(-b+-square root of b^2-4ac)/2a

x=(-6+-square root of 36-4.09)/2a here 4.09 came by calculation

x=(-6+-31.91)/2

so

x=(-6+31.91)/2 first (+);

x=25.91/2

x=12.955;

x=(-6-31.91)/2 then(-);

x=-37.91/2

x=-18.955 ;

ans is = 12.955&-18.955;

Answer:

∠AFE is an inscribed angle because the vertex lies on the edge of the circle

∠DOB is a central angle because the vertex lies at the center of the circle

∠HJG is an inscribed angle because the vertex lies on the edge of the circle

The person who worked out the first 31,415,926,535,897 digits of pi is not known.

However, there are several people who have contributed to its calculation over time. Some of the notable names include:

a. William Shanks (1812-1882), an English mathematician, was the first to calculate 707 digits of pi, but later calculations revealed that he made a mistake in the 528th digit. William Shanks (1812-1882) was an English mathematician who is known for his work on the calculation of pi. In 1853, he published a book titled "Contributions to Mathematics, Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals," in which he claimed to have calculated pi to 707 decimal places.

However, in 1945, it was discovered that there was an error in Shanks' calculation, and only the first 527 decimal places were correct. Despite this mistake, Shanks' work on the calculation of pi was still significant for its time, and he made important contributions to other areas of mathematics as well.

b. Richard Brent, an Australian mathematician, calculated the first 1,000,000 digits of pi in 1989 using a supercomputer. The current world record for calculating the most digits of pi is held by Timothy Mullican, who calculated over 31 trillion digits in 2019 using a cloud-based virtual machine.

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Answer:

Step-by-step explanation:

y + 4 = -3(x - 1)

y + 4 = -3x + 3

y = -3x - 1

Answer:

2

Step-by-step explanation:

(-8)÷(-1÷4) = 32

32/16 = 2

Answer:

(-8)÷(-0.25)÷(16)

Step-by-step explanation:

(a) The complementary solution, yc, for the associated homogeneous equation is yc(x) = C1e^(-3x) + C2e^(2x).

To find the complementary solution, we consider the homogeneous equation associated with the given differential equation, which is obtained by setting the right-hand side of the differential equation to zero. The general form of the complementary solution is in the form yc(x) = C1e^(r1x) + C2e^(r2x), where r1 and r2 are the roots of the characteristic equation. In this case, the characteristic equation is r^2 - 3r + 2 = 0, which has roots r1 = 1 and r2 = 2. Substituting these values into the general form gives us the complementary solution yc(x) = C1e^(-3x) + C2e^(2x).

(b) To find a particular solution, yp, using the method of undetermined coefficients, we assume that yp(x) has the form yp(x) = Ax + Be^(3x).

We assume that the particular solution has the same form as the non-homogeneous term, but with undetermined coefficients A and B. By substituting this assumed form into the original differential equation, we can solve for the coefficients A and B. After solving, we obtain the particular solution yp(x) = 2x + (27/10)e^(3x).

(c) To solve the initial value problem, we combine the complementary and particular solutions: y(x) = yc(x) + yp(x).

Given the initial conditions y(0) = 4, y'(0) = 13, and y''(0) = 33, we substitute these values into the general solution obtained in part (c). After evaluating the equations, we find the particular solution that satisfies the initial conditions: y(x) = (27/10)e^(3x) - (36/5)e^(2x) + 2x + 4.

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Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .

In the question ,

we have to find , whether a Right Triangle can be made by two fractions and an integer length .

yes, we can make a Right Triangle with two lengths as fractions and other length as integer .

let us prove it with the help of an example .

Consider the triplet 7 , 24 , 25 .

let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be  1 .

We know that for the Right Triangle

(side1)² + (side2)² = hypotnuse²

(7/25)² + (24/25)² = 1²

49/625 + 576/625 = 1

(49+576) / 625 =1

625/625 = 1

1 = 1

hence ,it is a Right Triangle .

Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .

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Answer:

4

Step-by-step explanation:

1 pi is not rationa;

2. sqrt20 is not rationa;

3.sqrt7 is not rational

4 is the answer

Number four is rational

Answer:

Step-by-step explanation:There are other kinds of numbers that can be graphed on the number line, too. ... which are natural numbers and which are whole numbers is to think of a “hole,” which can be represented by 0. ... Notice that distance is always positive or 0.

If x is the largest of the three consecutive integers, then the three consecutive integers can be represented as x-1, x, and x+1.

The sum of these three consecutive integers is:

(x-1) + x + (x+1)

Simplifying the expression, we get:

3x

Therefore, the expression in terms of the given variables that represents the sum of three consecutive integers when x is the largest is 3x.

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Y is constant.

The equation of line will be

Answer:

y=1

Step-by-step explanation:

Answer:

Sam made a mistake. The answer should have been 30.

This is what Sam should have done:

2n^2 - 20

2n^2 - 20 = 2(5)^2 - 20

= 2(25) - 20

= 50 - 20

= 30

Sam multiplied 2 and 5 when he should have done the power first.

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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Answer:

\(2x + 2 = 5x - 4 \\ 2x - 5x = - 4 - 2 \\ - 3x = - 6 \\ x = \frac{ - 6}{ - 3} \\ x = 2\)

Answer:

compounded continuously

Step-by-step explanation:

compounded continuously occurs more frequently than daily

Based on the formula that shows the change in altitude per minute, the number of minutes till the plane reaches and altitude of 21,000 feet is 6 minutes

The number of minutes the plane takes to reach 21,000 feet is:

Altitude = 3,400x time + 600

Solving for time gives:

21,000 = 3,400t + 600

3,400t = 21,000 - 600

t = 20,400 / 3,400

t = 6 minutes

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The order of visit for DFS and BFS will differ based on the structure of the graph or tree and the starting node. DFS will typically visit nodes in a deeper order, while BFS will visit nodes in a breadth-first order.

Both  algorithm depth-first search and algorithm breadth-first search are used to traverse or search a graph or tree data structure. The difference between them lies in their traversal strategy.
Depth-first search (DFS) starts at a root node and explores as far as possible along each branch before backtracking. It follows a content-loaded algorithm, meaning that it prioritizes exploring deeper into the structure before considering other branches. In terms of visit order, DFS starts at the root node, then moves to its first child node, and continues to explore its descendants until it reaches a leaf node. Once it has visited all descendants of the current node, it backtracks to the previous node and repeats the process until it has visited all nodes.
On the other hand, breadth-first search (BFS) starts at the root node and explores all the neighboring nodes at the current depth level before moving on to the next depth level. It follows a breadth-first algorithm, meaning that it prioritizes exploring all nodes at a given depth level before moving on to deeper levels. In terms of visit order, BFS visits all nodes at a given depth level before moving on to the next level.

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