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andreyandreev [35.5K]
3 years ago
13

What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47+ ...?​

Mathematics
1 answer:
Alex3 years ago
3 0

Answer:

\huge\boxed{18,475}

Step-by-step explanation:

The terms of this sum make the arithmetic sequence.

The fomula of a sum of <em>n</em> terms of an arithmetic sequence:

S_n=\dfrac{[2a_1+(n-1)d]\cdot n}{2}

We have

a_1=2\\d=17-2=32-12=47-32=15\\n=50

Substitute:

S_{50}=\dfrac{[2\cdot2+(50-1)\cdot15]\cdot50}{2}=(4+49\cdot15)\cdot25=(4+735)\cdot25\\\\=739\cdot25=18,475

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Given that the endpoints of a diameter are (7,-3) and (-1,7), determine the equation of the circle.
Margaret [11]

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^r

H and k are the x and y coordinates of the center of the circle and r is the radius.

You are given the diameter coordinates so find the halfway point for the center then calculate the radius

Midpoint = (x1 +x2)/2, (y1 + y2)/2

Midpoint = (7 + -1)/2, (-3 +7)/2

Midpoint = 6/2, 4/2

Midpoint = 3,2

So h = 3 and k = 2

Now find radius by finding the distance between the center point and an end point.

Distance = sqrt(41)

Equation of the circle:

(X-3)^2 + (y-2)^2 = 41

5 0
3 years ago
Read 2 more answers
The city of Raleigh has 9,200 registered voters. There are two candidates for city council in an upcoming election: Brown and Fe
sukhopar [10]

Answer:

A) The population of this survey is the registered voters in the city of Raleigh.

B) 9500

C) 200

D) 0.325

E) 3088

Step-by-step explanation:

A) The population of this survey is the registered voters in the city of Raleigh.

B) Population size can be defined as the total number of individuals in a population. Here the total number of individuals are the registered voters in the city. Therefore the size of the population is 9500.

c) Sample size is defined as the number of individual samples in a statistical test. Here the sample size is the 200 randomly selected registered voters. It is denoted as "n".

d) The sample statistic for the proportion of voters surveyed who said they'd vote for Brown would be:

p' = voters for brown / sample size

p' = \frac{65}{200} = 0.325

The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.325

E) The expected number of voters for Brown based on the sample:

0.325 * 9500 = 3087.5

Approximately 3088

The expected number of voters for Brown based on the sample might be 3088 voters.

7 0
3 years ago
Domain and range of the graph, is it a function?​
Elenna [48]

Answer:

  • domain: [0, ∞)
  • range: (-∞, ∞)
  • not a function

Step-by-step explanation:

The arrows indicate the graph continues indefinitely in the direction indicated.

The domain is the horizontal extent, so is the interval from 0 to infinity, including 0.

The range is the vertical extent, so extends from negative infinity to positive infinity (all real numbers).

The graph does not pass the vertical line test: a vertical line intersects it in more than one place, so the relation is NOT a function.

4 0
3 years ago
9. a. Maurice says that 1079 ÷ 62 is 16 with a remainder of 87. a. Without seeing his work, how can you tell Maurice divided inc
mamaluj [8]

Answer:

a.  We can tell that Maurice divided incorrectly because if the dividend is 62, you can't have a remainder of 87, because 62 goes into 87 once, so the answer would be 17 with a remainder of 25.  B. YOu can use that fact to find the correct quotient, because 87/62 is 1, with a remainder of 25, so 16+1=17, so the answer is 17 with a remainder of 25.   Please vote the brainliest.

Step-by-step explanation:

8 0
3 years ago
the temperature in winter night was -23 degrees Fahrenheit the temperature Rose by 5° when the sun rose when the sunset again th
expeople1 [14]

So we have -23 degrees to start

Then add 5 to it

It becomes -23+5=-18

Now subtract 7 from that so -18-7=-25 degrees

Hope this helps

8 0
3 years ago
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