Find a1 for the arithmetic series with s20 = 80 And d = 2

Answers

Answer 1

we know that
the formula of the arithmetic series is
Sn=n[2(a1) + (n - 1)d]/2
where
Sn=80
n=20
d=2
a1=?
then
80=20*[2*a1+19*2]/2----------------> 160=[40*a1+760]
160=[40*a1+760]----------> a1=(160-760)/40------------> a1=-15

the answer is
a1=-15

Answer 2

To solve this, we are going to use the standard formula for arithmetic series [tex]S _{n} = \frac{n}{2} [2a_{1} +(n-1)d][/tex]
where:
[tex]S_{n} [/tex] is the sum of the arithmetic sequence
[tex]n[/tex] is the number of terms
[tex]d[/tex] is the difference
[tex]a_{1} [/tex] is the first term
From our problem we know that [tex]S_{n} =80[/tex], [tex]n=20[/tex], and [tex]d=2[/tex]. Lets replace those values in our formula to find [tex]a_{1} [/tex]:
[tex]80= \frac{20}{2} [2a_{1} +(20-1)2][/tex]
[tex]80=10(2a_{1} +38)[/tex]
[tex]80=20a_{1} +380[/tex]
[tex]20a_{1} =-300[/tex]
[tex]a_{1} = \frac{-300}{20} [/tex]
[tex]a_{1} =-15[/tex]

We can conclude that the first term [tex]a_{1} [/tex] of the arithmetic series is [tex]-15[/tex]

Related Questions

Can someone help me? Please show your work.

Answers

We know that the perimeter of a rectangle can be represented by the expression 2l +2w, where l represents the length of the rectangle and w represents the width of the rectangle.

If we substitute in the values given in this problem, we get the expression:
2(2x+6) + 2(x)

Another equivalent expression we can use to express the perimeter is w + w + l + l.

If we substitute in the values given in this problem into this expression, we get:

x + x + 2x + 6 + 2x + 6

Overall, we know that these expressions are equivalent and represent the same value (the perimeter of the rectangle), because if you combine like terms, both expressions simplify to 6x + 12.

Hope this helps!

Brook says there are 49 days until july 4 there are 7 days in a week in how many weeks will it be until july 4

Answers

because 49 can be divided by 7 just divide the 49 days until july 4th by 7 in order to get 7 weeks left because you used the 7 in a week to divide into the amount of days left

7 weeks until July 4.

Calculating the Number of Weeks Until July 4

To determine in how many weeks it will be until July 4, given that there are 49 days left:

We know there are 7 days in a week.

We need to divide the total number of days by the number of days in a week.

The calculation is: 49 days ÷ 7 days/week.

Doing the division: 49 ÷ 7 = 7 weeks.

what is 68% out of 25

Answers

the answer to the question is 17

68% of a number= that number multiplied by 68/100
so 68% out of 25 = 25* 68/100 =17

Which equations represent hyperbolas?

Answers

Try this option:
1. Common view of hyperbola equation is:
[tex] \frac{x^2}{a} - \frac{y^2}{b} =1 \ , where \ a,b-numbers[/tex]
2. hyperbolas are: 2x²+4x-5y²-10y+57=0 and -x²+12x+3y²+7y+11=0.

Answer:

The correct options are 2 and 5.

Step-by-step explanation:

The general form of conics is

[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]

This equation represents the hyperbola if

[tex]B^2-4AC>0[/tex]

compare the given equations with the general equation.

In option 1,

[tex]A=2,B=0,C=2,D=16,E=14,F=-9[/tex]

[tex]B^2-4AC=(0)^2-4(2)(2)=-16<0[/tex]

This equation does not represents a hyperbola.

In option 2,

[tex]A=2,B=0,C=-5,D=4,E=-10,F=57[/tex]

[tex]B^2-4AC=(0)^2-4(2)(-5)=40>0[/tex]

This equation represents a hyperbola.

In option 3,

[tex]A=-1,B=0,C=-7,D=5,E=2,F=-81[/tex]

[tex]B^2-4AC=(0)^2-4(-1)(-7)=-28<0[/tex]

This equation does not represents a hyperbola.

In option 4,

[tex]A=0,B=0,C=-2,D=1,E=4,F=15[/tex]

[tex]B^2-4AC=(0)^2-4(0)(-2)=0[/tex]

This equation does not represents a hyperbola.

In option 5,

[tex]A=-1,B=0,C=3,D=12,E=7,F=11[/tex]

[tex]B^2-4AC=(0)^2-4(-1)(3)=12>0[/tex]

This equation represents a hyperbola.

Therefore the correct options are 2 and 5.

a used truck for $4,500 he made an agreement with the dealer to put $1,500 and make payments of 350 for the next 10 months that extra costs paid by taking this bill bill is equivalent to what actual yearly rate of interest

Answers

Ist amount paid = $1500
Making $350 for 10 months = 10*350 = $3500
Total amount paid = 1500 + 3500 = 5000
So an amount of $5000 was paid to cover the cost of $4500 within the ten month period.
I = PRT
Interest, I = 5000 - 4500 = 500Time, t = 10 months = 10/12 = (5/6) year.Principal P = 4500
R = I /(PT) R = 500 / (4500*5/6)
R = (500*6) / (4500*5)
R = 0.1333..
R ≈ 13.33 % per annum.

Kareem shot the basketball 32 times and made 23 baskets. What percent of his shots were baskets?

Answers

Percent of the shots that were baskets would be the number of baskets shot divided by the total number of shots multiplied by 100%.

The calculation will look like this:
number of baskets shot = 23 shots
the total number of shots =32 shots
Percent of the shots that were baskets= 23/ 32 * 100%= 71.875%

Answer:139%

Step-by-step explanation:

Given the functions, and g(x) = 3x 2 + 2, perform the indicated operation. f(g(x))

Answers

I’m not quite sure if I did this right,but 6x+3h

I believe the answer is 6x-13. But I'm not 100% posititive.

What is the coefficient of the variable in the expression 4 − 3x − 7 + 6?

Answers

A coefficient is the number directly in front of the variable, aka the number being multiplied with the variable. In this case it's -3.

Answer:

the coefficient is -3

Step-by-step explanation:

Find the product
54.88 x 7.3

Answers

54.88× 7.3=400.62 thats the answer

The answer is 400.624

What is the shape of the following distribution?

{9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 19, 20}

negative skew

postive skew

symmetric

asymmetric with no skew

none of the above

Answers

The first step is the summarize the data in tabular form. We have to mention the frequency of each number in front of it. For example, 19 occurs only once in the data, so the frequency of 19 will be one. The complete table is shown below.

On basis of this frequency table we can construct a histogram to visualize the data. The histogram is constructed and attached with. We can observe that the peak is at 4. There are fewer values on right side of the peak as compared to the left side of the peak. So more values tend to lie in left tail.

When there are more values in left tail we say that the data is left skewed or negatively skewed. So first option is the correct answer.

The distribution is positively skewed, as indicated by the longer tail on the right side of the dataset representing higher values.

The shape of the distribution for the dataset {9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 19, 20} can be determined by looking at the tail of the distribution. Since the values gradually increase and then have a longer tail towards the higher numbers (with the largest values occurring less frequently), we can identify this as a positively skewed distribution. The distribution does not display symmetry, and the tail extends more significantly to the right, which is indicative of a positive skew. This is because the bulk of the data is located on the left side (lower values), while the right side (higher values) stretches out longer due to the presence of outliers or a gradual decrease in frequency.

If there is a sphere with a volume of 1761.1 meters cubed, what is the radius?

Answers

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\quad \begin{cases} r=radius\\ -----\\ V=1761.1 \end{cases}\implies 1761.1=\cfrac{4\pi r^3}{3} \\\\\\ 3(1761.1)=4\pi r^3\implies \cfrac{3(1761.1)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{3(1761.1)}{4\pi }}=r[/tex]

Garys unpaid credit card balance is $2543.32. His APR is 17.4% qnd he made ine new transaction for $320 whats his new balance

Answers

New Balance = 2543.32(1 + 0.174/12) + 320 = 2543.32(1.0145) + 320 = 2580.20 + 320 = $2900.20

A political analyst predicts Mr. Smith will only get 122 votes for mayor. If Mr. Smith only gets 57 votes, what is the political analyst's percent error? Round your answer to the nearest tenth of a percent.

Answers

Final answer:

The political analyst's percent error is approximately 53.3%.

Explanation:

To find the political analyst's percent error, we need to calculate the absolute difference between the predicted votes and the actual votes, divide it by the predicted votes, and then multiply by 100. The formula for percent error is:

Percent Error = (|Predicted Value - Actual Value| / Predicted Value) * 100

Plugging in the values, we have:

Percent Error = (|122 - 57| / 122) * 100

Calculating the difference: |122 - 57| = 65

Calculating percent error: (65 / 122) * 100 ≈ 53.3%

Therefore, the political analyst's percent error is approximately 53.3%.

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Suppose the first class in a frequency table of quantitative data is 0 dash 40-4 and the second class is 5 dash 95-9. what is the class midpoint of the first class?

Answers

To get the class midpoint or the middle value of this problem, we need to get the average of the lower class and the upper class.So in formula it is = upper + lower / 2Our lower class is 0 while the upper class is 4. So 4 + 0 = 4/2 = 2 would be the answer.

Answer:

4 + 0 = 4/2 = 2 would be the answer.

Step-by-step explanation:

A company invests a total of $40 comma 000 of surplus funds at two annual rates of interest: 5% and 6one half %. It wishes an annual yield of no less than 6one fourth %. What is the least amount of money that the company must invest at the 6one half % rate? The company should invest at least $ nothing at 6one half %.

Answers

Suppose the company invests x of their surplus in the 5% rate (and thus 40000-x has 6.5%). Then we have that 5%*x+(40000-x)6.5%=6.25%*40000.
We have that solving this, 5%* x+40000*6.5%-6.5%*x =6.25%* 40000 Accumulating terms, 1.5%*x=0.25%*40000 x=40000/6= 6666.67$. We see that if we invest 6666.67$ at 5%, we get exactly the given rate. If we invest more, we obviously get less. Hence, we have that the company has to invest at 6.5% more than 40000-6666.67=33333.33$

preschool buys paint in bulk then divides the paint into smaller pirtions for use in the clasrooms. today they bought 4 2/3 gallons of green paint and divided it equally among 4 classrooms. how much green paint did each classroom get?

Answers

1.17 gallons of paint per room

Given: C is a point on the perpendicular bisector, l, of AB.

Prove: AC = BC

Answers

angles are never isoceles... may be you mean the triangle?
and also, what is C, where is it located? '

Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, BC. Using the definition of reflection, reflect BC over l. By the definition of reflection, C is the image of itself and A is the image of B. Since reflections preserve length, AC = BC.

Find the area of A circle whose diameter is 8.3m round to the nearest tenth

Answers

D=8.3

8.3/2 = 4.15

R=4.15

4.15* 4.15 * 3.14 = 54.07
HOPE THIS HELPS

Answer:

the answer is 54.1

Several shapes are cut out of a piece of cardboard. Two squares of length x, five rectangles of length x and width y and two circles with radius z. The two squares and four of the rectangles are glued together to form a prism, and the two circles and the remaining rectangle are used to form a cylinder with height y. Which represents the combined volume of the two figures?

Answers

the correct question in the attached figure

step 1
calculate the different volumes
a) Volume of prism square base=x*x*y=x²*y
b) Volume of the cylinder=π*(z²)*y

the combined volume of the two figures=[x²*y]+[π*z²*y]

the answer is [y*x²]+[π*y*z²]

If a pizza is cut into 8 pieces and 3 children each eat one piece, what fraction of the pizza is gone

Answers

the answer is 3/8
hope it helps
please mark as brainliest i need one more

3/8 is the fraction of pizza that is gone

The circumference of a circle is divided into twelve equal arcs. The measure of each arc is degrees.

Answers

For this case the first thing you should know is that a circumference measures the amount of 360 degrees.
If we divide the circumference into 12 equal arcs, each arc will have the following measure:
(360) / (12) = 30
Answer:
The measure of each arc is 30 degrees

Answer:

The measure of each of the arc in degrees is:

30 degree

Step-by-step explanation:

We know that the circle is a whole of 360 degrees.

Now when we divide the circumference of a circle into 12 equal arcs, then the measure of each arc in degrees is calculated as the ratio of the 360 degrees to the number of arcs it has been divided.

Hence, the measure of each arc in degrees is:

[tex]\dfrac{360}{12}=30[/tex]

Hence, the measure in degrees is:

30 degree

Janice really likes potatoes. potatoes cost $0.50 per pound, and she has $5.00 that she could possibly spend on potatoes or other items. suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30. instructions: enter your answers as whole numbers.
a. how many pounds of potatoes will she purchase?
b. what if she only had $3.00 to spend?

Answers

Final answer:

Janice will purchase 4 pounds of potatoes if she has $5.00. If she only has $3.00 to spend, she will purchase 3 pounds of potatoes.

Explanation:

To determine how many pounds of potatoes Janice will purchase, we need to subtract the cost of each pound of potatoes from her total budget until she no longer has enough money to purchase another pound. Let's go step by step:

Janice has $5.00 and the first pound of potatoes costs $1.50. After purchasing the first pound, she will have $5.00 - $1.50 = $3.50 left.

The second pound of potatoes costs $1.14, so she can buy the second pound and have $3.50 - $1.14 = $2.36 left.The third pound costs $1.05, so she can buy it and have $2.36 - $1.05 = $1.31 left.The fourth pound and any subsequent pounds cost $0.30 each. Since Janice has $1.31 left, she can afford $1.31 / $0.30 ≈ 4.37 pounds of potatoes.

Therefore, Janice will purchase 4 pounds of potatoes.

If Janice only has $3.00 to spend, we can follow the same steps:

With $3.00, she can afford $3.00 / $0.30 = 10 pounds of potatoes. However, since the value of each pound decreases after the third pound, she can only purchase the first three pounds. The fourth pound would cost $0.30, but she doesn't have enough money left.

Therefore, if Janice has $3.00 to spend, she will purchase 3 pounds of potatoes.

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How to subtract 546 from 735

Answers

It equals 189❤️❤️❤️hope that helps

735
546
--------

72 15
54 6
----------
9

6 12 9
4
------
689
5

189
This is the answer

Which values of P and Q result in an equation with exactly one solution? Qx-6=Px-103

Answers

Any values such that P ≠ Q will give an equation with exactly one solution.

Answer:

For any value of P & Q except when both are equal , we get One solution of equation.

Step-by-step explanation:

Given: Linear Equation, Qx - 6 = Px - 103

This equation has exactly 1 solution.

To find: Value of P and Q

First we solve the linear equation for value of x,

Qx - 6 = Px - 103

Transpose Px to LHS ( Left hand side ) we get,

Qx - Px - 6 = -103

Transpose 6 to RHS ( Right hand side ) we get,

Qx - Px = -103 + 6

Qx - Px = -97

taking x common in LHS, we get

( Q - P ) x = -97

Traspose ( Q - P ) to RHS, we get

[tex]x=\frac{-97}{Q-P}[/tex]

[tex]x=\frac{-97}{-(P-Q)}[/tex]

[tex]x=\frac{97}{P-Q}[/tex]

Thus, we are get only 1 value of x but it exist if P ≠ Q

otherwise no solution exist for the given linear Equation.

Therefore, For any value of P & Q except when both are equal , we get One solution of equation.

Marla says that every number in nineties is composite. Jackie says that one number in the nineties is prime. Who is correct?

Answers

Jackie. 97 is a prime number, not a composite.

Answer:

Jackie, 91, 97 is prime.

Step-by-step explanation:

Remember that a number greater than 2 is NOT prime if it is divided by any number different than 1, for example 6 is NOT prime because 3 divides 6. 7 is prime because the only divisors of 7 are 1 and 7.

So for the nineties 90 is divisible by 45.

91 is divisible by 7

92 is divisible by 2

93 is divisible by 3

94 is divisible by 2

95 is divisible by 5

96 is divisible by 2

97 IS PRIME, is just divisible by 1 and 97

98 is divisible by 2

99 is divisible by 3

Find the first four terms of this geometric sequence a1 = 5 And r = 6

Answers

general term of a geometric sequence is
a(n)=a(1)×r^(n-1)
a1=5
a2=5×6=30
a3=5×6²=180
a4=5×6³=1080

which ingredient does Ramon use the greater amount of, buttermilk or cream cheese? Explain how you found your answer.

( 5/8 cup buttermilk , 1/2cup cream cheese)

Answers

He uses more buttermilk.

1/2 is equal to 4/8
5/8 is greater than 4/8

62.5% = 5/8
50%= 1/2
so 5/8 is more

In a right triangle, cosA=0.352 and sinA=0.936 What is the approximate value of tanA?

A- 0.329
B- 0.376
C-1.288
D-2.659

Answers

The answer to this is: D. 2,659

Answer:

tanA=2.6591

Step-by-step explanation:

[tex]tanA=\dfrac{sinA}{cosA} \\\\tanA=\dfrac{0.936}{0.352} \\\\tanA=2.6591[/tex]

How many halves are in the following
12, 10, 13, 15,8 and 5

Answers

Since there are two halves in a whole, you can times each number by 2 to get the number of halves it has.

12*2=24
10*2=20
13*2=26
15*2=30
8*2=16
5*2=10

550 is 5% of what number?

Answers

27.5 if you divide 550by 5% you get 27.5

Oh, this is easy.

All you have to do is turn the 5% into a number. This is done by moving the decimal place two places to the left (the decimal place, in THIS case, is the percent sign). You get .05

Now, simply divide. Yes, this is a tricky part. When dealing with whole numbers and decimals, multiplecation is quite useless for cases like this, it simply makes the number SMALLER. If you want to find out what the ORIGINAL number was, you DIVIDE.

So, 550/.05

You get 11,000

This is your original number. That means 550 is 5% of 11,000

To check this, NOW use the inverse, multiplication. 11,000*.05=550

Your answer is 11,000

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