Write the following series in sigma notation.
7 + 16 + 25 +34 +43 +52 + 61

Answers

Answer 1

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

How to write the series in sigma notation?

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

First term, a = 7Common difference, d = 9Number of terms, n = 7

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7  - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]

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Related Questions

to the Kansas River Crossing.

Last year the depth of the river was 4.2 feet deep.

This year it dropped 17%.

Find the depth of the river this year to cross it.

Answers

Answer:

3.486 feet (1.06 m) or 3 feet (0.91 m) five inches

Step-by-step explanation:

17 percent of 4.2 is 0.714 and 4.2–0.714 is 3.486

Step-by-step explanation:

Solve the given system of differential equations by systematic elimination. Dx dt = 2x − y dy dt = x

Answers

The solution to the given system of differential equations is x(t) = t + C₁ and y(t) = t²/2 + C₁t + C₂.

1. dx/dt = 2x - y

2. dy/dt = x

Substituting y = -dx/dt into the second equation,

dy/dt = x - t

-d²x/dt² = x - t

Now, assume a particular solution of the form x = At + B,

where A and B are constants.

Substituting this into the differential equation,

-A = At + B - t.

Equating the coefficients of t on both sides,

A = -1 and B = 0.

Thus, the particular solution is x = -t.

Now, integrating dx/dt = -yt,

x = -yt + C₁

Finally, substituting x into the particular solution x = -t,

-t = -yt + C₁.

Solving for y, obtain y = t²/2 + C₁t + C₂.

Therefore, the solution is x(t) = t + C₁ and y(t) = t²/2 + C₁t + C₂.

Learn more about systematic elimination here:

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#SPJ4

Label the probabilities in the tree diagram below and determine what is the probability of wearing a red shirt and black jeans?

Answers

The probability of wearing a red shirt and a black jean is the likelihood of the shirt and jean

The probability of wearing a red shirt and a black jean is is 1/6

How to determine the probability?

From the tree diagrams, we have the following parameters

Total combination = 6

Red shirt and Black Jean = 1

The probability of wearing a red shirt and a black jean is calculated as:

P = n(Red shirt and Black Jean)/Total combination

This gives

P = 1/6

Hence, the probability of wearing a red shirt and a black jean is is 1/6

Read more about probability at:

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On Melissa's 6th birthday, she gets a $6000 CD that earns 7% interest, compounded semiannually. If the CD matures on her 14th birthday, how much money will be available?

Answers

if the CD matures on her 14th birthday, that means 8 years after she got it, since she got it in her 6th birthday, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &8 \end{cases} \\\\\\ A=6000\left(1+\frac{0.07}{2}\right)^{2\cdot 8}\implies A=6000(1.035)^{16}\implies A\approx 10403.92[/tex]

What is the standard form of the equation of a parabola that opens left or right? A. Y = ax2 + bx + c B. X = ay2 + by + c C. X = a(y - v)2 + h D. Y = a(x - h)2 + v

Answers

Answer:

The equation of the parabola which opens left or right is (B) x= ay^2 + by + c

:)

Is the figure defined by points H, I, J, and K a rhombus?

Yes, HIJK is a rhombus. Based on the coordinates, opposite sides are parallel, and all sides are congruent.
No, HIJK is NOT a rhombus. Based on the coordinates, opposite sides are parallel, but all sides are not congruent.
No, HIJK is NOT a rhombus. Based on the coordinates, all sides are congruent, but opposite sides are not parallel.
Yes, HIJK is a rhombus. Based on the coordinates, opposite sides are not parallel, and all sides are not congruent.

Answers

Answer:

b

Step-by-step explanation:

The area of a room is 26.025 m sqaure. If its length is 12.5m . find the breadth of the room​

Answers

Answer:

2.082.

Step-by-step explanation:

Solution,

Given,

Area ( A ) = 26.025 m².

Length ( L ) = 12.5 m.

Now,

Breadth ( B ) = Area ÷ Length.

= 26.025 ÷ 12.5

= 2.082.

Thus, The breadth of the room is 2.082 m.

please answer 100 points
Divide. 6 from 3/5
10
30
20
15

Answers

Answer:

Step-by-step explanation:

What is 6 divided by 3/56 ÷ 3 5. The trick to working out 6 divided by 3/5 is similar to the method we use to work out dividing a fraction by a whole number. ... 6 x 5 3 = 30 3. So, the answer to the question "what is 6 divided by 3/5?" ... 30 3. ... 10 1. ... 10 1 = 10.

Answer:

The numbers in 6 divided by 3/5 are labeled below:

6 = whole number

3 = numerator

5 = denominator

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:

6 x 5

3

 =  

30

3

Thus, the answer to 6 divided by 3/5 in fraction form is:

30

3

To make the answer to 6 divided by 3/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

30 / 3 = 10

The answer is rounded to the nearest two decimal points if necessary.

30/3 can be simplified to 10/1.

10/1 is an improper fraction and should be written as 10.Step-by-step explanation:

A student filled a right rectangular prism shaped box with one inch cubes to find the volume in cubic inches the students work is shown explain why the students reasoning is incorrect provide the correct volume in cubic inches and why the students reasoning is incorrect in your answer

Answers

The volume of the right rectangular prism is the amount of cubes in it

The formula to determine the volume of the right rectangular prism is V(n) = n

How to determine the volume?

The question is incomplete; as the figure is not given.

So, I will provide a general solution

The volume of a one inch cube is:

[tex]V = 1^3[/tex]

[tex]V = 1[/tex]

Assume the number of one inch cubes used to fill the right rectangular prism is n.

Then the volume of the right rectangular prism would be:

[tex]V(n) = n * 1[/tex]

This gives

[tex]V(n) = n[/tex]

Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n

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For the rotation 379°, find the coterminal angle from 0 <0 360°, the quadrant
and the reference angle,

Answers

To find the coterminal angle, it is similar to going around the entire circle once and then a bit more.

379 - 360 = 19

Coterminal Angle = 19 degrees

---All the way around and a bit more

Quadrant = 1

---Where the angle is

Reference Angle = 19 degrees

---Distance between the x-axis and the angle

Hope this helps!

Hi Mehta06 heres my question that i told you​

Answers

Answer:

1. WEA and and TSE

2.WES

3.50

Step-by-step explanation:

the inscribed angles are AWE, AWS, EST

As W is the center, ES is the Diameter

arc AE = 180-AWS

= 180-100

=80 degrees

MARK ME AS BRAINLIST

can anybody please help me with this math problem?

Answers

Answer:

  B.  (15, 19)

Step-by-step explanation:

To check to see if a particular ordered pair is a solution to an equation, use the values for the variables and see if the equation is true.

A. 4/5(0) +7 = 7 ≠ 1

B. 4/5(15) +7 = 19 . . . . . . is a solution

C. 4/5(-5) +7 = 3 ≠ 11

D. 4/5(-2) +7 = 27/5 ≠ 1

__

A calculator can help with this.

No chi-square The principal in Exercise 7 also
asked the random sample of students to record
whether they did all of the homework that was
assigned on each of the five school days that week.
Here are the data:
Monday Tuesday Wednesday Thursday Friday
School day
Number who did
all homework
34
29
32
28
19
Explain carefully why it would not be appropriate
to perform a chi-square test for goodness of fit using
these data.
oh

Answers

The random sample of the students is an illustration of sampling

The chi-square test for goodness of fit is inappropriate because the variable under study is not categorical.

How to determine the reason chi square is not appropriate?

The dataset is given as:

Monday        34

Tuesday       29

Wednesday   32

Thursday        28

Friday             19

The variable of the above dataset is a not a categorical dataset.

One of the conditions of the chi-square test for goodness of fit test is that the variable under study must be categorical.

Hence, the chi-square test for goodness of fit is inappropriate because the variable under study is not categorical.

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Could someone help, I need help with math, this is the question. The ratio of ducks to geese is 5:3. There are 50 ducks. How many geese are there?

Answers

ANSWER:
There are 30 geese.
STEP-BY-STEP EXPLANATION:
Let y be the total no. of animals
Share= ratio/total ratio X total
50= 5/8 X y
50= 5y/8
50 X 8= 5y
y= 400/5
y= 80
The total no. of animals is 80
80-50=30 ans.

please help: Simplify 6÷(4-2)+4

Answers

Answer:

7

Step-by-step explanation:

6/(2)+4

3+4

7(BODMAS)

But if you use calculator it we give you

5

A news report says that 28%
28
%
of high school students pack their lunch.
Your high school has 600
600
students.

How many students in your high school would you expect to pack their lunch?

Answers

you would do 600 x 28% then subtract what that equals from 600 to get the answer.
600 x 28% = 168
600-168= 432
you would guess that 432 students pack don’t pack lunch and 168 pack lunch

Solve: 2|x 7|−4 ≥ 0 express the answer in set-builder notation.

Answers

The correct answer for the given inequality is  {x | x ≤ -9 or x ≥ -5}.

What is inequality?

Inequality is a statement shows greater the, greater then equal to, less then,less then equal to between two algebraic expressions.

To solve an absolute inequality, first step is to isolate absolute value expression.

Hence remove -4 from the left side. So, add 4 to each sides of the inequality.

2|x + 7|−4 ≥ 0

2|x + 7|−4 +4≥ 0 +4

2|x + 7| ≥ 4 Combine the like terms.

Divide each sides by 2.

[tex]\dfrac{2|x + 7| }{2} \geq \dfrac{4}{2}[/tex]

|x + 7| ≥2

Next step is to remove the absolute value sign. So,

x + 7≥2 and x+7≤-2.

x≥2-7 and x≤-2-7

x≥-5 and x≤-9

So, the correct choice is  {x | x ≤ -9 or x ≥ -5}.

To know more about inequality, follow

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Answer:

1st one is: C

2nd one is: A

Step-by-step explanation:

please help i will give brainly?

Answers

Answer: $141.75

Explanation:

8:00-> 12:00= 4 hours

12:45->17:30= 5.45 hours

4+5.45=9.45 hours

9.45 x 15 = 141.75

if 45% of an item is 72.00 what is the original price. someone help me

Answers

Answer:

45% x 72.00 = 32.4

Step-by-step explanation:

hope this helped :)

Answer:

If 45% of an item is 72.00 what is the original price is, $160.00

Step-by-step explanation:

ABC has the following transformation rotated 90 degrees clockwise about the origin reflected across the y-axis and reflected again across the x-axis

Select the angle vertex that corresponds to angle A

Answers

Answer: Leftmost vertex

Step-by-step explanation:

A yurt, or circular tent, has a radius of 3 meters.

What is the area of the floor of the yurt?

Use 3.14 for π.

Enter your answer as a decimal in the box.

Answers

Answer:

area of yurt: 28.26 m²

formula:

area of circle: π * radius * radius

area of circle: πr²

solving steps:

(3.14)(3)²

28.26 m²

Answer:

Radius of the circular tent (r) = 3 m

Area of the floor = Area of circle = π r²/π =3.14

Area of the floor = 3.14 x 3² = 28.26 m²

Step-by-step explanation:

# Jerry Don is here#

what is math for

like what do we use it for whats the point of math no one uses it

Answers

Because,mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.

Answer:

The study of the measurement, relationships, and properties of quantities and sets, using numbers and symbols.

Step-by-step explanation:

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have what approximate shape?.

Answers

Using the Central Limit Theorem, the shape of the frequency curve will be approximately normal.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

Hence, the shape of the frequency curve will be approximately normal.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

A bakery sells chocolate cupcakes and vanilla cupcakes. It sold 143 chocolate cupcakes in a day. 35% of the cupcakes sold that day were vanilla. How many total cupcakes did the bakery sell that day?

Answers

Answer:220

Step-by-step explanation:

Change the following decimals to fractions give your answers in their simplest form a) 0.3 b) 0.46 c) 0.075

Answers

Answer:

[tex]0.3 = \frac{3}{10}\\\\ 0.46 = \frac{23}{50} \\\\0.075 = \frac{3}{40}[/tex]

Step-by-step explanation:

To convert decimals to fractions, you look at the place of the last digit of the fraction (i.e. the digit that the farthest right from the decimal)

For 0.3, 3 is in the tenths place, so we end up with the fraction [tex]\frac{3}{10}[/tex]

For 0.46, 6 is in the hundreths place, so before simplifying we have [tex]\frac{46}{100}[/tex]

The GCF of 46 and 100 is 2 so we divide the fraction by [tex]\frac{2}{2}[/tex] to get [tex]\frac{46}{100}[/tex] ÷[tex]\frac{2}{2}[/tex] = [tex]\frac{23}{50}[/tex]

For 0.075, the 5 is in the thousandths place, so before simplifying we have [tex]\frac{75}{1000}[/tex]

The GCF of 75 and 1000 is 25 so we decide the fraction by [tex]\frac{25}{25}[/tex] to get [tex]\frac{75}{1000}[/tex] ÷[tex]\frac{25}{25}[/tex] = [tex]\frac{3}{40}[/tex]

please help this question is hard (25 POINTS!!)

An experiment involves rolling two dice simultaneously. The following table shows the possible outcomes using the format of (die 1,die 2).

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

What is the probability of rolling 2 even numbers?

Enter your answer as a reduced fraction, like this: 3/14

Answers

Answer:

1/9

Step-by-step explanation:

Sum = 4: (1,3) (2,2) (3,1)

Sum = 12: (6,6)

4/36 = 1/9 or 0.111

hope that helps

Help help help help help help help help I just need the answer for 13, 15, 16

Answers

Answer:

13) Squares, Rectangles. 14) Rhombus, Square.

15) Parallelogram, rectangle, rhombus, square

Step-by-step explanation:

John drove 737 miles in 11 hours At the same rate, how many miles would he drive in 5 hours?

Answers

Answer:

Step-by-step explanation: 737/ 11= 67

sooooo 67 x 5= 335

What is the area of this polygon?

Answers

Answer:

The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].

Step-by-step explanation:

I hope I can help you:)

Roman purchased 2 1/2 pounds of chocolate covered peanuts for $9.75 what was the price per pound?

Answers

Answer:

$3.90

Step-by-step explanation:

2 1/2 pounds = 2.5 pounds

To determine the price per pound, divide $9.75 by 2.5:

[tex]\sf \dfrac{9.75}{2.5}=3.9[/tex]

Therefore, the price per pound was $3.90

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