Find the sum of the first 21 terms of the arithmetic progression.
−7, −11, −15, . . .

Answers

Answer 1

We are given with an AP (Arithmetic Progression) with first term being -7, and the common difference being the difference between any succeding term from any term and the term itself, so common difference = -11 - (-7) = -11 + 7 = -4, so now before finding the sum of 21 terms, let's recall that ;

[tex]{\boxed{\bf{S_{n}=\dfrac{n}{2}\{2a+(n-1)d\}}}}[/tex]

Where, d is the common difference, a is the first term, and n is the number of terms and [tex]{\bf S_n}[/tex], being the sum of n terms, so putting all the values in the formula, we will have ;

[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}\{2\times -7+(21-1)-4\}}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}(-8+20\times -4)}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-8-80)}{2}}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-88)}{2}}[/tex]

[tex]{:\implies \quad \sf S_{21}=-21\times 44}[/tex]

[tex]{:\implies \quad \boxed{\bf{S_{21}=-924}}}[/tex]


Related Questions

Given f(x)=5(x^2+1)+16, what is the value of f(11)?

Answers

Answer:

The value of f(11) is 9.

The function of a given term is a form of an expression where element of the domain consists of a unique identity and each input value of a function is allocated to only one output value.

From the parameters given;

we are to replace x with 11 wherever we see x

f(11) = 9

Step-by-step explanation:

What is the slope of a line perpendicular to the line whose equation is
5x – 2y = -10. Fully simplify your answer.

Answers

m=5/2

use the slope intercept y=mx+b

Which of the following steps would you perform to the system of equations
below so that the equations have opposite y-coefficients?
4x+2y - 4
12x - y - 26
O A. Divide both sides of the top equation by 3
O B. Multiply both sides of the top equation by 2
O C. Multiply both sides of the bottom equation by 2
O D. Divide both sides of the bottom equation by 3

Answers

Step-by-step explanation:

please mark as brainliest please

Felix buys five vests for $22 each, three pairs of shoes for $50 each, and six hats for $17 each. What is the mean amount that he spent?

A. $34.62
B. $32.81
C. $25.86
D. $22

Answer: C

Answers

Answer:

$ 25.86 is the answer

Step-by-step explanation:

All of the following are TRUE about CPR/AED EXCEPT:
A. CPR is used in emergency situations like a heart attack and near drowning.
B. CPR combines chest compressions and rescue breathing to increase the chance of survival.
C. CPR is guaranteed to keep a person alive until medical personnel arrive.
D. The use of an AED helps to restart the heart's natural rhythm.

Answers

Answer:

All are true except C. CPR is not a guarantee to keep someone alive till help arrives. Unfortunately some people die before help gets there regardless of the CPR.

A rectangular picture with perimeter 27 cm is glued in the center of a rectangular piece of cardboard. There is a 1 cm margin ( of empty cardboard) all around the picture. What is the perimeter of the piece of cardboard.

Answers

Answer:

  35 cm

Step-by-step explanation:

Each dimension of the picture is increased by twice the width of the margin. If the original picture has dimensions L×W, then the cardboard has dimensions (L+2)×(W+2).

The perimeter formula tells you the perimeter is ...

  P = 2(L +W)

__

The cardboard perimeter will be ...

  P' = 2((L +2) +(W +2)) = 2(L +W +4)

  P' = 2(L +W) +8

  P' = P +8

If the original perimeter is 27 cm, the cardboard perimeter is ...

  P' = 27 +8 = 35 . . . . cm

The perimeter of the cardboard is 35 cm.

F(x)= x^2+2, g(x)= x+1, and h(x) =2x what is f(g(x)) when x= -1

Answers

f(g(-1)) = (-1 + 1)^2 + 2
= 0^2 + 2
= 2

Your sister Samantha is turning 48 in April. She is 3 times older than your brother John, and twice as old as you. How old is your brother John?

Answers

Is john 16?
Since samantha is 48 and she is 2 times older than me, that means im 24 (48/2) and since 3 times older than john that means 48/3= 16. John is 16

What are the prime factors of 700?
O A.2 x 2 x 25 x 7
OB. 350 x 2
OC. 2 x 2 x 2 x 5x5x7
OD 2 x 2 x 5x5x7

Answers

Answer:

b. 350x2

Step-by-step explanation:

the answer is 350x2 because if you do 350x2 you will get 700

John and Monica completed the same task on different lines in an assembly plant. When John had completed 7/9 of the task, Monica had only completed 5/9 of the task. How much more of the task has John completed than Monica?

Answers

Answer:

2/9ths

Step-by-step explanation:

7/9 - 5/9 = 2/9

Hope this helps <3

A video game allows players to design their own character using the following options.
Video Game Character


What is the probability of designing a female character with long, red hair?

A. 1/24

B. 1/12

C. 1/9

D. 1/4

Answers

Answer:

1/24

Step-by-step explanation:

Probability of making female character = 1/2

Probability of having long hair = 1/3

Probablity of having red hair = 1/4

Multiply all these probabilities ( 1/2 x 1/3 x 1/4) = 1/24

The probability of making a female character with long red hair in this video game is 1 in 24.

I hope this helps.

Jaydon has eaten 3.6% his 45 ounce block of chocolate
fudge. How many ounces of fudge has he eaten?

Answers

Answer:

The answer is 1.62 ounce

Step-by-step explanation:

Given;Jaydon has eaten 3.6% of his 45 ounce block of chocolate fudge.To Find;How many ounces of fudge has he eaten?

Now,

3.6% of his 45 ounce

45 × 3.6 ÷ 100

162 ÷ 100 = 1.62

Thus, Jaydon has eaten 1.62 ounce block of chocolate fudge.

Round your answer to the nearest hundredth.

Answers

Answer:

66.42 degrees

Step-by-step explanation:

Cos(angle B) = adj / hyp = 2/5

arc cos (2/5) = angle B = 66.4 2 degrees

Describe the ratio of corresponding measures in scale drawing and the actual measure they represent

Answers

Answer:

More data needed.

Step-by-step explanation:

jijijijiji

Use the distributive property to express 30 + 42

Answers

Answer:

it would be  6 (5 + 7) = 30 + 42 = 72

Step-by-step explanation:

hope this helps if not please let me know

Among all rectangles that have a perimeter of 172, find the dimensions of the one whose area is largest. Write your answers as fractions reduced lowest terms.

Answers

Answer:

43 x 43  units      1849 units^2

Step-by-step explanation:

The largest area will be a square (equla sides)

   172 / 4 = 43

a square IS a rectangle

43  x   43

HELP ASAP 20 BRAINLY POINT PLUS USER HELPPP ​

Answers

Answer:

A

Step-by-step explanation:

(m / 3) = (12 / 3) = 4

1/2 x 4 = 2

2 + n = 2 + 3/5 = 2 and 3/5 = 13/5

Answer:

13/5

Step-by-step explanation:

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam Students who score in the top 26 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly
recognized?

Answers

Using the normal distribution, it is found that a student has to score 0.6433 standard deviations above the mean to be publicly recognized.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

The top 26% of the scores are given by scores above the 74th percentile, which corresponds to Z = 0.6433, hence, a student has to score 0.6433 standard deviations above the mean to be publicly recognized.

More can be learned about the normal distribution at https://brainly.com/question/24663213

The number 111…111 (100 ones) is multiplied by 101. The resulting number is then also multiplied by 101. The number obtained in the second step is again multiplied by 101. What is the sum of the digits of the number obtained in the third step?

Answers

Answer:

  800

Step-by-step explanation:

The three multiplication steps are equivalent to multiplying by ...

  101³ = 1030301

The sum of digits of the product will be the sum of digits of the partial products, since none of the digit-by-digit multiplications results in a product that is more than 10.

The sum of digits of the third product is ...

  (1 × 100) × (1 + 3 + 3 + 1) = 800

Rewrite the equation below so that it does not have fractions.
3+ 2/3 x = 2/5

Answers

Answer:

3 + 2 divided by 3 = 2 divided by 5

Step-by-step explanation:

Evaluate F ( 3 ) :
F ( 3 ) =
X =

Answers

Answer:

f(3) = 1

x = 2

Step-by-step explanation:

f(2) = 3 then x = 2

Please ,Check the illustration I provided.

1 + a to the power 3
[tex]1 + {a}^{3} [/tex]

Answers

Explanation:

Given that, 1 to the power of 3
Generally, the rules for exponentiation states that if l is any real number and m is a positive integer, then lm can be shown as:

lm = l × l × … × l (m times)

Hence, 1 to the power of 3 can be written as 13, where the number 1 is called the base, and 3 is the power or exponent of the expression.
Therefore, 13 = 1 × 1 × 1 = 1

Hence, 1 to the power of 3 comes as 1.

3. What function can be used to model data pairs that have a common ratio? (1 point)

O linear
O quadratic
Oexponential
Onone of the above

Answers

Answer:

The function that can be used to model data Paris that have a common ratio is exponential.

common ratio exponential

1/4*3/4=what is the answer​

Answers

Answer:

3 over 8

3

8

=0.375

Step-by-step explanation:

please help me statistic and probability​

Answers

Answer:

Probability of 15 = 3/10

Probability of 14 = 2/10

Probability of 10 = 2/10

Probability of 12 = 1/10

Probability of 20 = 1/10

Probability of 25 = 1/10

Step-by-step explanation:

→ Find how many numbers there are

2 14's, 3 15's, 2 10's, 1 12, 1 20 and 1 25 ⇒ The x value row will be 14, 15 ,10 ,12, 20 and 25

→ Now divide each front number by the total

Probability of 15 = 3/10

Probability of 14 = 2/10

Probability of 10 = 2/10

Probability of 12 = 1/10

Probability of 20 = 1/10

Probability of 25 = 1/10

Simplify the expression.
a)1/64
b)2^-30
c)64
d)2^30

Answers

[tex]\left(\dfrac{(-1)^5}{(-2)^{-3}} \right)^2\\\\\\=\left(\dfrac{-1}{\dfrac{1}{(-2)^3}} \right)^2\\\\\\=\left(-1 \times -8\right)^2\\\\=8^2\\\\=64[/tex]

Answer:

[tex]\huge\boxed{\bf\:64}[/tex]

Step-by-step explanation:

[tex]\left(\frac{(-1)^{5}}{\left(-2\right)^{-3}}\right)^{2}[/tex]

Now, simplify [tex](-1)^{5} = -1[/tex]. Then,

[tex]\left(\frac{-1}{\left(-2\right)^{-3}}\right)^{2}[/tex]

Calculate: [tex](-2)^{-3} = \frac{1}{(-2)^{3}} = - \frac{1}{8}[/tex].

[tex]\left(\frac{-1}{-\frac{1}{8}}\right)^{2}[/tex]

Divide [tex]-1[/tex] by [tex]- \frac{1}{8}[/tex]. The result will be [tex]8.[/tex]

[tex]\left(-\left(-8\right)\right)^{2} \\= 8^{2}[/tex]

Calculate [tex]8[/tex] to its square which is [tex]64.[/tex]

[tex]8^{2}\\=\boxed{\bf\: 64} \: \:\mathrm{(3^{rd} \: option)}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Need help as soon as possible

Answers

Answer:

100cm

Step-by-step explanation:

divide the shape into smaller shapes then find the area of each and add them together

Find the area of this parallelogram.
A) 20 B) 24 C) 40 D) 60

Answers

[tex]\underline{\clubsuit{\bf{Given-}}}[/tex]

Height of the Parallelogram = 4cm

i.e, H = 4cm

Breadth of the Parallelogram = 10cm

i.e, B = 10cm

Measure a side of the Parallelogram = 6cm.

PS - Neglecting this because it is given just to puzzle us nothing else.

[tex]\underline{\clubsuit{\bf{To\:find-}}}[/tex]

the area of the Parallelogram.

[tex]\underline{\clubsuit{\bf{Concept-}}}[/tex]

Area of Parallelogram Formula

A parallelogram's area is defined as the space enclosed by two pairs of parallel lines. Since a rectangle and a parallelogram have identical properties, the area of a parallelogram equals the area of a rectangle.

What's the procedure to find?

To find the area of the parallelogram, we have to multiply the base (denoted by B) of the perpendicular by its height (denoted by H). We should keep in mind that the base and the height of the parallelogram are perpendicular to each other, whereas the lateral side of the parallelogram is not perpendicular to the base. Thus, a dotted line is drawn to represent the height.

— Formula

Area of Parallelogram = Breadth (B) × Height (H)

[tex]\underline{\clubsuit{\bf{Solution-}}}[/tex]

Applying the formula and putting the values stated above,

[tex]\rightarrow{\sf{Area=10\times4}}[/tex]

[tex]\rightarrow{\boxed{\bf{Area=40cm^2}}}[/tex]

Hence, the area of the Parallelogram is 40cm².

Question - I need more ----- inside of my life

Answers

Answer:

Hi, this is not really a question it is a statement but if you really need help with math then you can provide an actual question.

Step-by-step explanation:

Answer:

Then you must improve to get more things in your life

In the U.S. it is implied that two-year schools (community colleges) are “a bargain” compared to 4-year institutions. Complete a two-sample test. Test that the “average cost of state universities is greater than the average cost of community colleges”. To perform this test, you will use the average cost of in-state tuition from your sample data of state universities. ($10,472) You will also need to find the mean and standard deviation from the random sample of community colleges provided below. To find the mean and standard deviation for the community colleges data, plug the values into L1 and run 1-varstats. The mean is x-bar and make sure to use sample standard deviation, Sx. Assume variances are NOT equal as is done in the example on page 430. Complete a two-sample test at α = 0.05. WRITE AN INTERPRETATION OF YOUR RESULT. use either the p-value decision rule or rejection region. show all work by hand (If you establish in the hypothesis that 1 is the universities and 2 is community colleges make sure that your x-bar 1 and x-bar 2 also reflect those same categories. ) In hypothesis tests, I am looking for the correct conditions, hypotheses, model of either decision rule (draw out the normal distribution with correct shading of either p-value or rejection region), correct formula for the standardized test statistic with all values plugged in correctly, correct decision based on your p-value or standardized test statistic, and correct interpretation of your findings.
In-State Tuition

Amarillo College

2,538.00

Blue Ridge Community College

4,098.00

Bunker Hill Community College

3,384.00

Camden County College

1,650.00

Delta College

2,400.00

Eastern Wyoming College

2,280.00

Ellsworth Community College

3,960.00

Finger Lakes Community College

3,894.00

Granite State College

6,810.00

Massachusetts Bay Community College

3,624.00

Rock Valley College

2,970.00

San Antonio College

3,632.00

Answers

Answer: I got the same question, did u get the answer?

Step-by-step explanation:

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