1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
shusha [124]
2 years ago
7

The sum of the first 15 terms of an arithmetic series

Mathematics
1 answer:
ale4655 [162]2 years ago
7 0

Answer:

d=4

Step-by-step explanation:

SUM OF 15 terms = 615

T5 = 53

T5 = a+(n-1)d

53 = a + 4d

4d = 53 - a

d = (53-a)/4

S15 = 15/2 (2a+14d) =615

15/2 [2a + 14×(53-a)/4 ]

=15/2 [ 2a +(53×14 - 14a )/4 ]

=15/2 [ (8a +742 - 14a ) /4]

615×8 = 15(-6a +742)

-6a+72=615×8/15 =41

-6a+72=42

-6a = - 72 + 42 = -30

a = 30/6= 5

a = 5

T5 = 5 + 4×d = 53

4d= 53 - 5 = 48

4d=48

d=4

Common difference is 4

You might be interested in
Kelvin measured the distance from his door to the park. It is 1.5 miles. The distance from Kelvin’s house to the library is twic
valkas [14]

Answer:

2.25

Step-by-step explanation:

1.5x1.5= 2.25

it is 1.5 mi from kelvins door to the park, it is 2.25 mi from kelvins house to the library.

hope this helps, let me know if you need more explaining

8 0
3 years ago
The cost of a pen is 3 times the cost of a pencil and cost of a
valentinak56 [21]

Answer:

1 Pen cost $2.25

Step-by-step explanation:

Assume:

Cost of Pen = a

Cost of pencil = b

Cost of notebook = c

a = 3b   -------------------(1)

c = 4a   -------------------(2)

2a + 6b + c = $18 -----(3)

From equation (1), b = a ÷ 3 ---------(4)

Substitute equations (2) and (4) in equation (3)

2a + 6 * (a ÷ 3) + 4a = $18

2a + 2a + 4a = $18

8a = $18

a = $2.25

Therefore, 1 Pen cost $2.25

6 0
3 years ago
This is 5th grade math pls help
Mamont248 [21]

Answer:

He can make 20 cakes

Step-by-step explanation:

Im in highshool so I know the answer

3 0
3 years ago
Read 2 more answers
Suppose I collected a sample and calculated the sample proportion. If I construct a 90% confidence interval for the population p
Daniel [21]

Answer:

Step-by-step explanation:

If you construct a 90% confidence interval for the population proportion and a 95% confidence interval for the population proportion, the 95% confidence will have a wider interval. This is because a higher confidence interval will provide more possible values from which the true value will be determined. Therefore, If you want more confidence that an interval contains the true parameter, then the intervals will be wider.

3 0
3 years ago
The hypotenuse of a 45 -45 -90 triangle measures 128 cm what is the length of one leg of the triangle
erma4kov [3.2K]
This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.
4 0
4 years ago
Read 2 more answers
Other questions:
  • Draw the prime factor tree for: 169 and 555 PLEASE PLEASE PLEASE PLEASE HELP!!!!!!!!!!!!!!!!
    7·1 answer
  • A retailer buys pants at $28.00 and sells them for $42.00. The percent of markup on cost is
    14·2 answers
  • How to combine fractions 5b/4a+b/3a-3b/a
    9·1 answer
  • Suppose a triangle has sides a, b, and c, and let (/) be the angle opposite the side of length a. If cos(/) > 0 what must be
    7·2 answers
  • Given the following sequence, find the 14th term: 3, 1, –1, –3, –5, . . .
    10·1 answer
  • Circle A has a radius of 4 units
    7·1 answer
  • How much more popcorn does the bigger box hold than the smaller box??
    12·2 answers
  • A lottery has a prize valued at $2400 and k tickets are sold at $2.00 each. Express the expected value of a ticket as function o
    12·2 answers
  • Add 8x+6yz-3zx, 4yz+6zx-8y, -3xz+6x-4xy<br><br> pls find answer...
    10·1 answer
  • Please help me, image below, thank you!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!