Answer:
an =6n
Step-by-step explanation:
6, 12, 18, 24
Take the 2nd number minus the first number, 3rd minus the second, etc
12-6 =6
18-12 = 6
24-18 =6
The common difference is 6
The formula for an arithmetic sequence is
an =a1+d(n-1)
where a1 is the first term
d is the common difference
n is the term number
an = 6+6(n-1)
Distributing
= 6+6n-6
= 6n
Answer:
She uses 200 milliliters of solution B
Step-by-step explanation:
Notice that there are two unknowns in this problem: 1) the amount of solution A that is being used, and 2) the amount of solution B being used. We can name such unknowns with letters to facilitate our work:
Amount of solution A to be used = A
Amount of solution B to be used = B
So, since we need to find two unknowns, we need to create a system of two equations to solve them.
Our first equation can be obtained from the sentence: "She uses twice as much Solution A as Solution B," which written in mathematical form is:
A = 2 B
The second equation we can build from the information of the amount of alcohol in each solution that combined will add up to 104 milliliters of alcohol in the mixture. Knowing the percent of alcohol in each solution, we can write an equation for the amount of alcohol:
0.19 A + 0.14 B = 104
Now we can use our first equation to substitute A in terms of B in the second equation:
0.19 (2 B) + 0.14 B = 104
0.38 B + 0.14 B = 104
0.52 B = 104
B = 104 / 0.52
B = 200 milliliters
C. Both options A and B will allow him to meet his goal.
Looking at Drake's situation after 4 weeks, he only has $470 saved. By
his original plan, he should have had $500 saved. So he's $30 short of
his goal and has 2 weeks until his originally planned class. If he goes
with option A and takes the later class, he will save an additional $125
which is more than enough to make up the $30 short fall. So option A
will work for him to save enough money for his class. With option B, he
will save $140 for the last 2 weeks of his plan giving him a savings of
$280 for the last 2 weeks. Adding the $470 he's already saved will give
him a total savings of $470 + $280 = $750 which is enough for him to
attend his class. So option B will also allow Drake to attend his
desired class. Both options A and B allow him to meet his goal. Hence,
the answer is "c".
