d = 3 , a₁₂ = 40 and S
= 7775
In an arithmetic sequence the nth term and sum to n terms are
<h3>• a

= a₁ + (n-1)d</h3><h3>• S

=

[2a + (n-1)d]</h3><h3>
where d is the common difference</h3><h3>a₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3</h3><h3>a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40</h3><h3>S₁₀₀ =

[(2×7) +(99×3)</h3><h3> = 25(14 + 297) = 25(311)= 7775</h3>
The attached diagram represents the Venn diagram of the sets
<h3>How to draw the Venn diagram?</h3>
The sets are given as:
- The universal set, U = The set of integers.
- A = The set of even integers.
- B = The set of odd integers.
- C = The set of multiples of 3.
- D= The set of prime numbers
From the above representation, we have the following highlights:
- Set A and set B will not intersect, because no number can be even and odd
- Set C and set D will intersect set A because they have common elements 6 and 2, respectively
- Set C and set D will intersect set B because they have common elements 3 and 3, respectively
Using the above highlights, we can now draw the Venn diagram
See attachment for the Venn diagram
Read more about Venn diagram at:
brainly.com/question/4910584
#SPJ1
Assigning "a" as cost of adult tickets and "c" the cost of children's tickets.
3a + 4c = 107
2a + 3c = 76
elimination method
2(3a + 4c = 107)
-3(2a + 3c = 76)
6a + 8c = 214
-6a - 9c = -228
----------------------
0 - c = - 14
c = 14
Then 2a + 3(14) = 76
2a = 76 - 42
2a = 34
a = 34/2
a = 17
If you have 8 yellow balloons for every 12 blue balloons, then if you have 20 balloons in total, 8 out of 20 of those balloons will be yellow. Then you can set up this ratio.
Then, you can use either cross multiplication or multiply the numerator and denominator by the same number to help solve for x. Personally, I prefer cross multiplication.
Finally, solve for x and if you had 100 balloons, you will have 40 yellow balloons.