Given:
First term of an arithmetic sequence is 2.
Sum of first 15 terms = 292.5
To find:
The common difference.
Solution:
We have,
First term: 
Sum of first 15 terms: 
The formula of sum of first n terms of an AP is
![S_n=\dfrac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
Where, a is first term and d is common difference.
Putting
, n=15 and a=2 in the above formula, we get
![292.5=\dfrac{15}{2}[2(2)+(15-1)d]](https://tex.z-dn.net/?f=292.5%3D%5Cdfrac%7B15%7D%7B2%7D%5B2%282%29%2B%2815-1%29d%5D)
![292.5=\dfrac{15}{2}[4+14d]](https://tex.z-dn.net/?f=292.5%3D%5Cdfrac%7B15%7D%7B2%7D%5B4%2B14d%5D)
![292.5=15[2+7d]](https://tex.z-dn.net/?f=292.5%3D15%5B2%2B7d%5D)
Divide both sides by 15.




Dividing both sides by 7, we get


Therefore, the common difference is 2.5.
Answer:
$33.00
Step-by-step explanation:
Total number of members = 45+30 = 75
Total cost for making name tags
= 75 * (0.44)
= $33.00
Answer:
120 000 m^2
Step-by-step explanation:
I ASSUME you're being asked to convert from km^2 to m^2.
For this you need to identify the conversion rate, which is 1 000 000 m^2 / 1 km ^2. Multiply by the thing you're converting from and cancel the units.
(1 000 000 m^2 / 1 km ^2) x 0,12 km^2 = 120 000 m^2 (the km^2 cancels out, leaving you only with your target unit of m^2)
Answer:
a. -2
b. s = 2 and y = -5
c. (2.5, -9)
d. -7x - 2
Step-by-step explanation:
a. In the image, I have used rise over run, which is -8/4 or -2.
b. slope formula is mx + b = y, where m is slope and b is the y-intercept. In the equation 2x - 5y = -10, 2 is the slope and -5 is the y-intercept.
c. Plug in all given numbers into an equation and the ones you do not have will be in the points you need it to be. Once you graph the equation you will receive (2.5, -9).
d. y = mx + b
5 = (-7)(-1) + b
5 = 7 + b
-2 = b
y = -7x - 2
Answer:
≈ 78.55 cm
Step-by-step explanation:
Using the ratio of arc (AB) to circumference (C) is equal to the ratio of angle subtended at centre by arc AB to 360°, that is
=
, that is
=
( cross- multiply )
110C = 8640 ( divide both sides by 110 )
C =
≈ 78.55 cm ( to 2 dec. places )