EVALUATE EACH OF THE FOLLOWING. LEAVE ANSWER IN REDUCED FRACTION FORM. DO NOT LEAVE ANSWER IN DECIMAL FORM.A) _6C6_8C0 = __________

5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

Learn more about sequence at

brainly.com/question/29591699

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

Find out more on fractions here: https://brainly.com/question/78672

#SPJ1

Answer:

7

Step-by-step explanation:

To find the median, put all numbers into ascending order and work into the middle by crossing off numbers at each end. If there are a lot of items of data, add 1 to the number of items of data and then divide by 2 to find which item of data will be the median.

Answer: 7

Step-by-step explanation:

1. put them in order from least to greatest = 2, 3, 6, 6, 7, 8, 8, 8, 15

2. find the number in the middle = 7

Hope I helped, have an amazing day!!

Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

1.43

Step-by-step explanation:

12 tenths ⇒ 1.2

23 hundredths ⇒ 0.23

0.23 + 1.2 = 1.43

the difference of elevation between a and b.Let AB = x, tan 36 = x/111.356 ,x = 111.356 tan 36= 64.39 m and Difference in elevation = 64.39m

We are given that two ridges B and C form a valley with a point A at the bottom part with an elevation difference of 111.356m between the ridges and and angle of elevation of 36 degrees at point A. To find the difference of elevation between A and B, we use the formula of tangent which is tan θ = Opposite/Adjacent. We substitute the values and solve for x, which is the elevation difference between A and B. So the difference in elevation between A and B is 64.39m.

Learn more about elevation difference here

https://brainly.com/question/6689872

#SPJ4

Answer: C (A unimodal histogram, and the dotted line lands at 210)

Step-by-step explanation:

Khan Academy - “The sample size is reasonably large (n = 30 _> 30), so the sampling distribution of x will be approximately normal even though the population isn’t.”

Answer:

70*pi

Step-by-step explanation:

No idea mate

Answer:

Step-by-step explanation:

circumference of a circle = 2πr

where

r = 70/2 = 35 yd

π = 3.14

plugin values into the formula:

C = 2 (3.14) 35

C = 219.8 yd.

Answer: The probability would be zero

Step-by-step explanation:

There are two children and one is a boy, so the probability of both being girls is a zero

Darren needs approximately 49 feet of tape.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

P = 2(L + W)

P = 2(10 + 8)

P = 2(18)

P = 36 feet.

In Mathematics and Geometry, the perimeter of a semicircle can be calculated by using this mathematical equation:

P = 2(π × radius)

P = 2(3.14 × 8/4)

P = 2(6.28)

P = 12.56 feet.

Approximate length of tape = 12.56 feet + 36 feet

Approximate length of tape = 48.56 ≈ 49 feet.

Read more on perimeter of a rectangle here: brainly.com/question/28695033

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The equivalent expressions are given below;

a) x²+3x+5

b) x²-3x+5

c) 3x³+15x

d)  x²+5/3x

Given the following function

f(x)=x²+5 and;

g(x)=3x

a) (f + g)(x) = f(x) + g(x)

(f + g)(x) = x²+5 + 3x

(f + g)(x) = x²+3x+5

b)  (f - g)(x) = f(x) - g(x)

(f - g)(x) = x²+5 - 3x

(f - g)(x) = x²-3x+5

c) (f * g)(x) = f(x) * g(x)

(f * g)(x) = 3x(x²+5)

(f * g)(x) = 3x³+15x

d) (f/g)(x) = f(x)/g(x)

(f/g)(x) = x²+5/3x

This expressions gives the equivalent answer.

Learn more on operations of functions here: https://brainly.com/question/17043948

#SPJ4

Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

To know more about Originality.

https://brainly.com/question/31916017

#SPJ11

The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

Learn more on parallel and perpendicular lines here: https://brainly.com/question/29526529

#SPJ1

Answer:

Width: 22.53 in.

Length: 28.35 in.

Step-by-step explanation:

If the perimeter is 101.76 in, we can create an equation of 2l + 2w = 101.76 in (length is l, and width is w). We also have that the rectangular painting is 5.82 in taller than it is wide. We can create a new equation stating that l = w + 5.82. We can now substitute l for w + 5.82 into our original equation, 2l + 2w = 101.76, and we get 2(w + 5.82) + 2w = 101.76. Now simplify and get 4w + 11.64 = 101.76. Simplifying this the whole way, we get w = 22.53. Now plug this value of w back into the equation, l = w + 5.82, and we get l = 22.53 + 5.82 = 28.35. We now have width: 22.53 in. and length: 28.35 in.

The smallest number that will make it divisible by 11 is n = 2 and the number is A = 7,01,69,302

Given data ,

Let the missing number be represented as n

Now , the value of the original number is A = 7,01,69,30*​

where * represents = n

To make a number divisible by 11, the difference between the sum of the digits in the odd-numbered positions and the sum of the digits in the even-numbered positions must be a multiple of 11.

On simplifying the equation , we get

To make the difference between the sums a multiple of 11, we need to add the smallest digit to the end. The smallest digit is 8

Hence , the number that is divisible by 11 is 7,01,69,302

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

For more such questions on data.

https://brainly.com/question/30459199

#SPJ8

Answer:

2/5 or 0.4.

Step-by-step explanation:

6/15 = 2/5

Answer:

Either 8% or 12%.

Step-by-step explanation:

For the given function the value of limits are

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\) is 5

\(\lim _{x\to 0^+}\left(f\left(x\right)\right)\) is 0

\(\lim _{x\to 0}\left x^2+5\)is 5

The given function is f(x)= x²+5, when x≤0

f(x)=2x when x>0

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0^-}\left x^2+5\)

The given limit is a left hand limit as there is minus in the limits

When we apply x as 0 we get the value 5

Now \(\lim _{x\to 0^+}\left(f\left(x\right)\right)\)

So \(\lim _{x\to 0^+}\left 2x\)

The given limit is a right hand limit as there is positive in the limits

When we apply x as 0 we get 0

Now \(\lim _{x\to 0}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0}\left x^2+5\)

We get 5

To learn more on Limits click:

https://brainly.com/question/8533149

#SPJ1

Answer:

f(-5) = 22

Step-by-step explanation:

f(x) =-3x+7

Let x = -5

f(-5) =-3*-5+7

      = 15 +7

       =22

The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments

From the question, we have the following parameters that can be used in our computation:

The table of values

For the membership application, we have the following features

So, the function is

f(x) = 600 - 10x

For the membership available, we have the following features

So, the function is

g(x) = 20/3x

So, the functions are f(x) = 600 - 10x & g(x) = 20/3x

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

The formula that defines the sequence is f(n) = f(n-1) + 4

The recursive function rule is expressed as;

f(n) = f(n-1)  + d

where

d is the common difference

Given the following sequence

2, 6, 10, 14, 18..

Determine the common difference

d = 6-2 = 10-6

d = 4

Substitute to have

f(n) = f(n-1)  + d

f(n) = f(n-1) + 4

Hence the formula that defines the sequence is f(n) = f(n-1) + 4

Learn more on recursive formula here: https://brainly.com/question/1275192

#SPJ1

Answer is 7.b  because of the angles

Answer:

It would be just f(x)=(4x+3) as the +2 in the original equation is translating the graph 2 units up from the x-axis

Step-by-step explanation:

f(x)=(4x+3)+2

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

f(x)=(4x+3)

The required length of AC in triangle ABC is b = 119.57 units.

In triangle ABC, we have:

\($\angle B = 85^\circ$\)

\($\angle C = 53^\circ$\)

\($BC = 85 units\)

AB = c

AC = b (we need to find the value of b)

We know that the sum of the interior angles of a triangle is \($180^\circ$\). Therefore:

\($\angle A = 180^\circ - \angle B - \angle C$\)

\($\angle A = 180^\circ - 85^\circ - 53^\circ$\)

\($\angle A = 42^\circ$\)

Using the law of sines, we have:

\($\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$\)

Substituting the given values, we get:

\($\frac{c}{\sin 85^\circ} = \frac{b}{\sin 53^\circ}$\)

Solving for $c$, we get:

\($c = b \cdot \frac{\sin 85^\circ}{\sin 53^\circ}$\)

We also know that:

\($\frac{a}{\sin A} = \frac{85}{\sin 42^\circ}$\)

Solving for a, we get:

\($a = 85 \cdot \sin 42^\circ$\)

Now we can use the law of cosines to find b:

\($b^2 = a^2 + c^2 - 2ac \cdot \cos B$\)

Substituting the known values, we get:

\($b^2 = (85 \cdot \sin 42^\circ)^2 + \left[b \cdot \frac{\sin 85^\circ}{\sin 53^\circ}\right]^2 - 2 \cdot 85 \cdot b \cdot \sin 42^\circ \cdot \sin 85^\circ/(\sin 53^\circ)$\)

Simplifying and solving for b, we get:

b = 119.57 units

Therefore, the length of AC in triangle ABC is b = 119.57 units.

To know more about Triangle visit:

brainly.com/question/2773823

#SPJ1

Answer:

10% of 100=10

20%of 100=20

5% of 100=5

50%=50

125

Answer:

first of all come to 1/4  1 divide by 4 is 0.25 now come to 12-4x its (8x) now brackets mean divide so 0.25 divide 8x is 0.3125 = now equation b x has no value so we will minus 3 from the brackets value 3 - 0.3125 =2.6875 THEREFORE 0.3125=2.6875

Step -by-step explanation:

Step-by-step explanation:

Team A time is    1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr

Team B =   1 / ( 1/3 + 1/3) =  1 1/2 hr

Team A wins !