The sequence (a_n) is defined recursively by a_1 = - 36, a_n+1 = a-n/2 + 72/a-n 1) Find the term a_3 of this sequence. a3 = _________
2) Prove by induction that for all n ∈ N, a_n < 0.

Answer: - 7 1/3 or -88/12 (it depends)

Step-by-step explanation:

To solve this equation, multiply the second number using it's reciprocal. A reciprocal is a flipped version of a fraction.

(3/4 to 4/3)

-22/4  x  4/3 = -88/12

Change it to a mixed number.

-7 1/3

Therefore, - 7 1/3 is the answer to this problem or keep it as -88/12.

Answer: 9x + 17

Step-by-step explanation: Add 4x and 5x and you get 9x. Next take away 15 from 32 and you get 17 therefore the answer wuld be 9x + 17.

Does the graph represent a function and if so, why: B. Yes, no two ordered pairs on this graph have the same second element.

In Mathematics and Geometry, a function refers to any mathematical equation which is typically used to define and represent a relationship that exists between two or more variables such as an ordered pair, points on a graph or table.

Based on the graph, we can reasonably infer and logically deduce that the relation represent a function because the input values are uniquely mapped to the output values.

In this context, we can conclude that the graph represents a piecewise-defined function because none of the two ordered pairs on this graph are having the same second element.

Read more on function here: brainly.com/question/27862183

#SPJ1

Therefore, the mean increases by 2.7°. Therefore, the median stays at 77.9°. Therefore, the median decreases from 86.5° to 88.5°.

The mean, also known as the average, is a measure of central tendency in statistics. It is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values.

Here,

1. To find out how adding a value of 110.5° to the data affects the mean, we need to calculate the original mean and then the new mean with the additional value included:

Original mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 ≈ 80.4°

New mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 110.5) / 13 ≈ 83.1°

Answer: The mean increases by 2.7°.

2. To find out how adding a value of 48° to the data affects the median, we need to first calculate the original median:

Arrange the data in order: 57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

The median is the middle value, which is 77.9°

Now, we add 48° to the data:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 48

Arrange the data in order: 48, 57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

The median is still the middle value, which is 77.9°

Answer: The median stays at 77.9°.

3. If a value of 71° is changed to 93°, the measure that changes the most is the median.

To find the new median, we need to first sort the data:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

The original median was the average of the two middle values, which were 79 (77 and 82). If we change 71 to 93, the new sorted data would be:

57, 58, 61, 66, 77, 82, 91, 93, 95, 100, 102, 105

The new median would be the average of the two middle values, which are now 88.5 (82 and 91).

4. If a value of 103° is added to the data, the mean increases by 8.6°.

To see this, we first need to calculate the original mean of the data:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 80.4

Then, we can add 103 to the data and calculate the new mean:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 103) / 13 = 89

The difference between the original mean (80.4) and the new mean (89) is 8.6, so the correct answer is: The mean increases by 8.6°.

To know more about mean,

https://brainly.com/question/14724376

#SPJ1

The following diagram shows the number of people who know the riddle per day.

The values of x would be from day 1 to 6 while the values of y will be 5, 20, 60, 240, 960, 3840. Thus, we may write the following in the table as follows:

Notice that 5 is always multiplied by a power of 4.

Thus, on day 1, we have

On day 2, we have

On day 3, we have

On day 4, we have

On day 5, we have

And on day 6, we have

Therefore, we may say that the formula to obtain the number of people who know the riddle on x days will be

where y is the number of people and x is the number of days.

Therefore, on the 15th day, we substitute 15 to x in the obtained equation.

Therefore, there will be 1,342,177,280 people who will know the answer on the 15th day.

The number of travel books sold each month is 1598.

To find the number of travel books sold each month, we need to multiply the total number of books sold by the percentage of books that are in the travel category.

The given pie chart shows the distribution of the most popular book categories sold by Book Street Books, expressed as percentages of the total number of books sold each month.

The percentage of books sold that are travel books is 47%, so we need to multiply 0.47 by the total number of books sold

Number of travel books sold = 0.47 x 3400

Multiply the numbers

= 1598

Rounding this to the nearest integer gives us

Number of travel books sold each month = 1598

Learn more about percentage here

brainly.com/question/12715980

#SPJ4

The given question is incomplete, the complete question is:

Book street books sells about 3400 books each month. the pie chart displays the most popular book categories, by percentage, each month. find the number of travel books sold each month. round your answer to the nearest integer.

Answer:

-1 i think

Step-by-step explanation:

Answer:

g=12/7

Step-by-step explanation:

The areas of section 1, 2 and 3 are  8 inches square, 80 inches square and 8 inches square respectively.

The area of the trapezium is 96 inches square.

Section 1 and 2 are right triangles.

Area of a right triangle = 1/2 x base x height

Height = 8cm

Base = (14 - 10) / 2 = 2cm

Area of a right triangle = 1/2 x 2 x 8 = 8cm²

Section 3 is a rectangle.

Area of a rectangle = length x width

8 x 10 = 80 cm²

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Area of a trapezoid =   1/2 x (sum of the lengths of the parallel sides) x height

= 1/2 x (10 + 14) x 8

1/2 x 24 x 8 = 96cm²

To learn more about trapeziums, please check: https://brainly.com/question/25044638

#SPJ1

Answer:

≈ 19.1 feet

Step-by-step explanation:

A right triangle is formed by the building , the ground and the ladder , that is the hypotenuse.

let x be the distance foot of ladder is from the building.

using Pythagoras' identity in the right triangle

x² + 34² = 39²

x² + 1156 = 1521 ( subtract 1156 from both sides )

x² = 365 ( take square root of both sides )

x = \(\sqrt{365}\) ≈ 19.1 feet ( to the nearest tenth )

Answer:

It is R, T.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I got it right

The slopes for each segment are given as follows:

The lengths of each segment are given as follows:

Hence DE = 0.5 = AC, and thus DE is the midsegment of triangle ABC.

The slope of a set of two points is given by the change in y between the two points divided by the change in x between the two points.

Both segments in this problem, DE and AC, are horizontal lines, meaning that the change in y is of zero while the change in x is different of zero, thus the slope is calculated as follows:

Slope = Zero/Constant different of Zero = Zero.

The lengths of each of the horizontal segments is obtained subtracting the x-coordinates, as follows:

More can be learned about slopes at https://brainly.com/question/8062156

#SPJ1

Answer:

C 47.12 L

Step-by-step explanation:

1 gallon = 3.8 liters

12.4 gallons = x

Cross Multiply

= 12.4 × 3.8

47.12 liters

Option C is correct

Answer:

13, 39

Step-by-step explanation:

H +J =52

H=3J

3J +J=52

4J=52

J=52 :4 =13 (Jane is 13

H =3 ×13 =39 (Harvey is 36

Parallel lines have the same slope, so the slope is 5.

The equation in point-slope form is y-10=5(x-3). Substituting x=0, we get y - 10 = -15, and thus the y intercept is (0, -5).

Step-by-step explanation:

7+8+10=25cm is the possibile perimeter of this

triangle.

Answer:

Angle C is the opposite angle of AB

Side AB is opposite to angle ∠ACB in triangle ABC

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given rectangle, AC is the diagonal

ABC and ADC are two right triangles.

We have to find the angle which is opposite to the side AB.

The angle opposite to side AB is angle C.

In the option we have angle ∠ACB.

Hence, Side AB is opposite to angle ∠ACB in triangle ABC

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ2

Answer:

200

Step-by-step explanation:

Answer:

Area =  l × w

=  18 × 10

=  180 centimeters2

Step-by-step explanation:

The rate of change is found using the slope formula

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

We have two points

( 1995, 2.54) ( 2010, 3.18)

m = (3.18-2.54) / (2010-1995)

=.64/15

$.042666666 per year

Rounding to the nearest cent

$.04 per year

We know that the price went up from 1995 to 2010 so the price increased

It increased an average of $.04 each year

A. The price of a gallon of gasoline increased by an average of $_.04__ per year from 1995 to 2010

Longitudinal parity is sometimes called longitudinal redundancy check question is b. horizontal. Longitudinal parity is a type of error-checking method used in digital communications.

It involves adding an extra bit to each data word to ensure that the total number of 1s in the word, including the parity bit, is always even or odd. This allows the receiving device to detect if there has been an error during transmission.

Longitudinal parity is also sometimes referred to as longitudinal redundancy check or horizontal parity. In conclusion, the correct term to fill in the blank in your question would be "horizontal".

To know more about horizontal., visit:

https://brainly.com/question/29019854

#SPJ11

Answer:

The answer is 293.57.

Hope you do great!

Step-by-step explanation: The way you do it is by seeing the 100% of any number and subtracting the 30% off and then divide the number by 70% and then multiply that number by the original 100%!

Answer:

1) 4·(n + 9) = 4·n + 4·9; Distributive Property

2) (6·7)·m = 6·(7·n); Associative Property of Multiplication

3) b · 1 = b; Multiplicative Identity Property

4) a + (-a) = 0; Additive Inverse Property

Step-by-step explanation:

1) The given equation and the properties that justifies the equation are;

4·(n + 9) = 4·n + 4·9

The above equation can be written as follows;

4 × (n + 9) = 4 × n + 4 × 9

Therefore, the common factor, 4 is distributed across the to the two terms inside the parenthesis, which gives the property as distributive property

2) (6·7)·m = 6·(7·n)

The above equation gives the association of the product of the  first two terms on the left multiplied by the third term being equal to the product of the first term and the association of the product of the last two terms on the right of the term on the right hand side of the equation

Therefore, we have associative property of multiplication

3) b · 1 = b

The value of the product of any variable and 1 is the value of the variable

Therefore, we have the multiplicative identity property

4) a + (-a) = 0

The sum of a variable (or number) and the negative (or opposite) of the variable (or number) is 0

Therefore, we have the additive inverse property

The value of is 1.645. This is derived from the area under the normal curve between 0 and 1.645 being equal to 0.25, which is one-fourth of the total area under the entire curve.

To calculate this, we must first understand the concept of the Standard Normal Distribution. The Standard Normal Distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This is the basis of the calculation.

Next, we need to understand the concept of the cumulative probability density function. This is a function that gives the probability that a variable will take a value that is less than or equal to a given value.

For our calculation, we will use the cumulative probability density function for the Standard Normal Distribution.

Now, to calculate the value of , we can use the cumulative probability density function. We will set the cumulative probability density function equal to 0.25.

This is the probability that a variable will take a value that is less than or equal to . Solving for, we get 1.645. This is the value of.

For more questions like Normal curve visit the link below:

https://brainly.com/question/12867171

#SPJ4

Rounded to the nearest inch, we get 434 inches cubed.

To determine the radius of the sphere before you can determine its volume. You can calculate the diameter by taking the diameter of 29.5 inches and dividing it by pi.

Let the equation be

\($\begin{gathered}C=\pi \times D \\\frac{29.5}{3.14}=\frac{1475}{157}=9.3949044585987261\end{gathered}$$\)

Then divide the diameter by 2 to get the radius.

\($\frac{\left(\frac{29.5}{3.14}\right)}{2}=\frac{1475}{314}=4.6974522292993631$$\)

So we get a radius of about 4.70.

Then we Utilize the formula for the volume of a sphere which exists

\($V=\frac{4}{3} \times \pi \times r^3$$\)

Substituting in R for 4.69, we get

\($\frac{4}{3} \times 3.14 \times\left(\frac{1475}{314}\right)^3=433.96579644880793$$\)

Rounded to the nearest inch, we get 434 inches cubed.

Therefore, the correct answer is 434 inches cubed.

To learn more about surface area refer to:

https://brainly.com/question/1297098

#SPJ1

If we round to the next inch, we get 434 inches cubed. The three-dimensional equivalent of the two-dimensional circle, a ball is spherical and has a sphere-like shape.

Suppose the equation is  \(C = \pi \times D\)

\(\frac{29.5}{3.14} =\frac{1475}{314} = 9.3949044522293\)

Next, multiply the radius by two to obtain the diameter.

\(\frac{\frac{29.5}{3.14}}{2} =\frac{1475}{314} = 4.6974522293\)

Consequently, we determine that the radius is around 4.70. Next, we use the formula for the volume of a sphere that is known.

\(V= \frac{4}{3} \times \pi \times r^{3}\)

When we replace 4.69 with R, we obtain , We get 434 inches cubed when we round to the nearest inch.

Basketballs typically have a surface size of 277.6 square inches. Calculate the basketball's circumference. Use the alumrof aera ecafrus formula, which is the reverse of the surface area formula. A basketball has a circumference of roughly 4.7 inches. The circumference of a basketball can be used to determine its volume. Basketballs used in the official NBA have a 29.5-inch circumference and a 434-cubic-inch capacity.

To learn more about surface area refer to :

https://brainly.com/question/16519513

#SPJ1

Answer:

-12

Step-by-step explanation:

-4x + -12 = -12

Answer:

f(x) = 2x + 4 domains {-1, 0, 1}

range {2, 4, 6}

(please mark brain if this helps and is correct)

Step-by-step explanation:

to solve f(x) to find the range you would want to input all the domain numbers in the equation f(x) to get the range of all the numbers you need

step 1: take the first domain number and input it into your equation where x is

ex: 2x + 4   [2(-1) + 4] = -2 + 4 = 2

step 2: add the second domain number and input it into your equation where x is

ex: 2x + 4   [2(0) + 4] = 0 + 4 = 4

step 3: add the last domain number and input it into your equation where x is

ex: 2x + 4   [2(1) + 4] = 2 + 4 = 6

Now we have determined what the range is

Answer:

-18

Step-by-step explanation:

6-12=-6-12=-18

The integers closest to the number is "68 < 69 < 70". This is the complete statement.

To complete the statement "< 69 <", we need to fill in the missing number in the middle.

Since 69 is the given number, we need to find the integers that are closest to it. The two integers closest to 69 are 68 and 70.

This means that the number 69 is between 68 and 70, and it is the middle number in the given range.

Learn more about integers here: https://brainly.com/question/33503847

#SPJ11