An arithmetic sequence has first term (a) and the common difference (d). The sum of the first 25 terms is 15 times the sum of the first 4 terms. Find (a) ​

Answers

Answer 1

Answer:

a = 12.

Step-by-step explanation:

Sum of n terms = n/2[2a + d(n-1)]

For 25 terms

S25 = 12.5(2a + 24d)

S25 = 25a + 300d

For 4 terms

S4 = 2(2a + 3d)

So:

S25 = 15*2(2a + 3d)

S25 = 60a + 90d

25a + 300d = 60a + 90d

35a =  210d

a = 6d

Take  a to be 12 and d to be 2:

25th term = 12.5(2*12 + 24 * 2) = 900

4th term = 2(24 + 6) = 60

900 = 15 * 60 so a = 12.


Related Questions

Describe what you normally do on Sunday​

Answers

Nothing just lay in bed all day on my phone-

my normal routine except i go to church

A. y=-2x+6
B. y=2x +6
C. y= -1/2x +6
D. y=1/2x+6

Answers

Answer:

A. y=-2x+6

Step-by-step explanation:

On a test that has a normal distribution, a score of 32 falls three standard
deviations below the mean, and a score of 82 falls two standard deviations
above the mean. Determine the mean of this test.

Answers

Answer:

Mean = 62

Step-by-step explanation:

X = mean ± sd

82 = mean + 2(s.d) - - (1)

32 = mean - 3sd ___(2)

82 = mean + 2sd

82 - 32= 2sd + 3sd

50 = 5sd

sd = 50/5

sd = 10

From (2):

32 = mean - 3sd

32 = mean - 3(10)

32 = mean - 30

32 + 30 = mean

62 = mean

Calculate the distance between the points K = (1, -1) and P=(9.-6) in the coordinate plane.
Give an exact answer (not a decimal approximation)

Answers

Answer:

√89

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(9 - 1)² + [-6 - (-1)]²

√(8)² + (-5)²

√64 + 25

√89

3 apples cost $1.00. How many apples for $2.00

Answers

Answer:

6 apples

Step-by-step explanation:

3 apples cost $1.00

so for $2.00, 2x3÷1=6

hope it helps. plz mark me as brainliest.

Answer:

6 apples

Step-by-step explanation:

if three apples are 1 dollar then every time you add a dollar you would get three more apples

so it would look somthing like

1$ = 3 apples

2$= 6 apples

3$= 9 apples  

4$= 12 apples

so on

A pool manager balances the pH level of a pool. The price of a bucket of chlorine tablets is $90, and the price of a pH test kit is $11. The manager uses a coupon that applies a 40% discount to the total cost of the two items. How much money does the pool manager pay for each item?

Answers

Answer:

The chlorine tablets are $36 and the pH test kit is $4.40.

Step-by-step explanation:

So what I first did was add 90+11 (because $90 for the chlorine tablets and $11 for the pH kit). The answer you should get is 101.  From their I did 101 multiplied by 40% or 101 multiplied by .40 (40% and 0.40 are the same thing). You now get $40.4.  

Now I did 90·40%. I got $36

Then I did 11·40%. I got 4.4

I added them up and got $40.4 which was my new price so now we know that the chlorine tablets are $36 and the pH test kit is $4.40.

The product of two numbers is 342. If one number is 18, what is the other nnumber without the use of a calculator show all your steps

Answers

342/18 18 x 10= 180 342 - 180= 162 18 x 9= 90 + 72= 162 10+9= 19 The answer is 19

in which situation would hydrogen bonding be present?
A. When hydrogen exists as an ion in solution
B. When hydrogen is attached to C, S or P
C. When hydrogen atoms bond together to form H2
D. When hydrogen is attached to N, F or O​

Answers

Answer:

D

Step-by-step explanation:

lol this is a weird math question

jk

Hydrogen bonds occur only when hydrogen is covalently bonded to one of three elements: fluorine, oxygen, or nitrogen. Anything else isn't considered a hydrogen bond.

Find the unit rate.
2 2/5 to 3 3/4

Answers

Answer:

2 2/5=5/5+5/5+2/5=12/5

3 3/4= [(3•4)+3]/4=15/4

(12/5) / (15/4)= 12/5 • 4/15=12•4/5•15=

48/75 kilometers in 1 minute

Step-by-step explanation:

How that this helps! :)

Have a great rest of your day/night!

(200 x 3) + (50 x 3)

Answers

200x3=600

50x3=150

600+150=750

750

A system of equations is created by using the line that is created by the equation 3x-2y=-4 and the line that is created
by the data in the table below.
Х
y
-9
-3
-1
-5
3
3
5
7
What is the y-value of the solution to the system?

Answers

Answer:

y=6x-8

Step-by-step explanation:

3x-2y=-4

3x^2-2y^2=-4^2

6x-y=8

y=6x-8

Find the length of the missing side.
7
24

A 25
B.168
C 31
D. 625

Answers

Answer: C

Step-by-step explanation: #1 because if you add 24 and 7 it looks like the other side.

Answer:

A. 25

Step-by-step explanation:

By Pythagoras theorem,

[tex] {25}^{2} = {24}^{2} + {7 }^{2} \\ 625 = 576 + 49 \\ 62 5= 625 \\ therefore \: 25 \: is \: the \: correct \: \: answer.[/tex]

Which of the following equations is represented by a line passing through (-9, 7) and (3, 3) in the
standard (x, y) coordinate plane?

Answers

Answer:

y = -1/3x + 4

Step-by-step explanation:

(-9, 7) and (3, 3)

Slope:

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

m=(3-7)/(3+9)

m=(-4)/12

m= -1/3

Slope-intercept:

y - y1 = m(x - x1)

y - 7 = -1/3(x + 9)

y - 7 = -1/3x - 3

y = -1/3x + 4

Step-by-step explanation:

[tex]soln \\ \frac{3 - 7 }{3 - - 9} \\ = \frac{ - 4}{ - 12} \\ = \frac{1}{3 } \\ \frac{y - 7}{x - 3} = \frac{1}{3} \\ then \: you \: cross \: multiplication. \\ 3(y - 7) = 1(x - 3) \\ 3y - 7 = x - 3 \\ 3y = x - 3 + 7 \\ 3y = x + 4 \\ \frac{3y}{3} = \frac{x}{3} + \frac{4}{3} \\ y = \frac{x}{3} + \frac{4}{3} [/tex]

You spin the spinner and flip a coin. Find the probability of the compound event. The probability of spinning a number less than 3 and flipping tails is

Answers

Answer:

1/5

Step-by-step explanation

The spinner has the numbers 1-5 and they want the numbers less than 3 there a 2/5 then multiply the denominator by 1/2 thin divide it by 2

2/10 divided by 2 = 1/5

.

(50 POINTS) Write out each sum.

Answers

Step-by-step explanation:

12. n^2+2n

if you insert 1 for k and then work up by inserting 2 for k and adding those together and stoping at n.

13. 8-2(2^n)

if you insert 3 for k and then work up by inserting 4 for k and adding those together and keep on going but stopping at n.

Hope that helps :)

Which value below represents the solution to 64 = 4u

Answers

Answer:

You didnt write the options

Answer:

u=16

Step-by-step explanation:

64=4u

divide both sides by 4

16=u

HELPPPPPPP
What is the value of x?

Answers

I.) 8
180 - 140 = 40.. divide that by 5 since it’s 5x, which’ ll leave you with 8.

Answer:

the angles are supplementary

so, 5x + 140 = 180

5x = 180 - 140

5x = 40

X = 40

5

X = 8

Which of the following expressions results in 0 when evaluated at x = 3?

(x + 3)(x + 12)

(x + 20)(x - 3)

-20x(x + 3)

(x + 8)(x - 5)

Answers

(X+20)(x+ 3). Put 3 in for x.

"You go shopping and notice that 25 kg of PEI’s Famous Potatoes cost $12.95, and 10 kg of Idaho’s Potatoes cost $5.78.

Which is the better deal?

Justify your answer."

Answers

Answer:

PEI famous potato is a better deal

Step-by-step explanation:

Given that :

PEI potato :

25kg costs $12.95

Price per kg :

$12.95 / 25 = $0.518 per kg

IDAHO Potato :

10kg costs $5.78

Price per kg:

$5.78 / 10

= $0.578 per kg

0.518 < 0.578

Hence, PEI famous potato is a better deal

Find b given that A (-6, 2), B (b, 0), and C (3,-4) are collinear.

Answers

Answer:

b = -3.

Step-by-step explanation:

If the 3 points are collinear then:

Slope of AB = Slope  of BC and so

(0-2)/(b + 6) = (-4-0)/( 3 - b)

-4(b + 6) = -2(3 - b)

-4b - 24 = -6 + 2b

-24 + 6 = 2b + 4b

6b = -18

b = -3.

[48 (72-12) -225] ÷ 9

someone pls help​

Answers

Answer:

295

Step-by-step explanation:

Answer:

295!

Step-by-step explanation:

72 - 12 = 60

48 x 60 = 2880

2880 - 225 = 2655

2655 / 9 = 295

Have you ever heard of PEMDAS? It is the order in which to solve equations like this one. Here's what it stands for:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

I hope this is helpful for future math equations similar to this one.

PR and os are diameters of circle T. What is the

measure of SR?

50°

* 80°

• 100°

120

Answers

Answer:

100degrees

Step-by-step explanation:

Find the diagram attached

From the diagram

<PQT =<TRS = 40

Since the triangle STR is isosceles, here,

<TSR =<TRS = 40

Also the sum of angle in a triangle is 189, hence:

Arc SR+<TSR +<TRS = 18₩

ArcSR +40+40=180

ArcSR +80=180

ArcSR = 180-80

ArcSR = 100degrees

Hence the measure of SR is 100degrees

The measure of arc SR is 100°. The correct option is the third option - 100°

Calculating the measure of an Arc

From the question, we are to determine the measure of arc SR.

The measure of arc SR = <STR

Now, we will determine the measure of <STR

In the diagram, T is the center of the circle.

TP and TQ are radii.

Then, we can conclude that ΔPQT is an isosceles triangle.

Recall: Base angles of an isosceles triangle are equal.

∴ <PQT = <TPQ = 40°

Now, consider ΔPQT

<QTP + <TPQ + <PQT = 180° (Sum of angles in a triangle)

<QTP + 40° + 40° = 180°

<QTP + 80° = 180°

<QTP = 180° - 80°

<QTP = 100°

Also, in the diagram, <QTP and <STR are vertically opposite angles

NOTE: Vertically opposite angles are equal

That is, <QTP = <STR

∴ <STR = 100°

Hence, the measure of arc SR is 100°. The correct option is the third option 100°

Learn more on Calculating the measure of an arc here: https://brainly.com/question/3506007

Here is the complete and correct question:

Line PR and Line QS are diameters of circle T. What is the measure of Arc SR?

50°

80°

100°

120°

Please find the attached image

Least:
Greatest:.
Median
Lower Quartile Range:
Upper Quartile Range:
thx :)

Answers

Answer:

Below :)

Step-by-step explanation:

Least/Minimum: 0

Greatest/Maximum: 6

Median: 2

Lower Quartile Range: 1

Upper Quartile Range: 3

Find median:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6

Find Lower Quartile:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2

Find Upper Quartile:

2, 2, 3, 3, 3, 3, 4, 4, 4, 6

10 people can paint a building in 5 days. If each person paints as quickly as the others then how much of the building could 7 people paint in 5 days?


A.7/5
B.5/7
C.7/10
D.10/7

Answers

Answer:

C

20 character minimum

HELPPPPPPPPP
What is the value of x in the figure at the right?

Answers

Answer:

x=30

HOPE THIS HELPS

-Todo <3

Step-by-step explanation:

60=2x

/2   /2

30=x

How to write 0.00080 as a power of 10?

Answers

Answer:

8 × 10⁻⁴

Step-by-step explanation:

using the equation y=x , what would be the value of y if the value of x is 2

Answers

Answer:

y = 2

Step-by-step explanation:

y = x

x = 2

Plug in the given value.

y = (2)

This is already simplified.

Therefore, when x = 2, y = 2.

Hope this helps!

Please help me with this questions please please ASAP ASAP please ASAP help please please ASAP please I'm begging you please please ASAP

Answers

Answer:

Question 3: 8000

Question 4: 300

Answer:

3. 8,000

4. 300

Step-by-step explanation:

3.

2/5 * 20,000 = 2 * 20,000/5 = 2 * 4,000 = 8,000

Answer: 8,000

4.

Use a proportion.

10/2 = x/60

5/1 = x/60

x = 5 * 60

x = 300

Answer: 300

True or False: When conducting a survey of a group of people, you must interview every person in that population A Truc B False​

Answers

A. its true.........

a business woman bought a personal computer for $108000.calculate her selling price on the personal computer if she wants to make profit of 25%​

Answers

Answer:

$135,000

Step-by-step explanation:

108000*1.25

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