Mathematics: Correct answer only ! andrew earns an allowance of $12 the first week, $17 the next week, $22 the following week, and so on. how much will andrew earn over the course of 10 weeks?

Correct answer only ! andrew earns an allowance

s11632270

09.03.2022

$345

Step-by-step explanation:

The explicit rule for an arithmetic sequence is: $a_n=a_1+d(n-1)\ \text{where}\ a_1\ \text{is the first term and d is the difference}$

In the given problem, a_1=12 and d = 5

$a_n=12+5(n-1)\\.\quad=12+5n-5\\.\quad=5n+7\\\\a_{10}=5(10)+7\\.\quad=50+7\\.\quad=57$

The sum of an arithmetic sequence is: $S_n=\dfrac{a_1+a_n}{2}\cdot n$

$S_{10}=\dfrac{12+57}{2}\cdot 10\\\\.\quad=69\cdot 5\\\\.\quad=345$

0,0(0 оценок)

travyse

22.11.2022

After 3.27 hours trains will meet up.

Step-by-step explanation:

When two trains are moving on parallel tracks in the same direction then their relative speed will be = Difference of their speeds

And when two trains travel on parallel tracks in the opposite directions then their relative speed is calculated as = Sum of their speeds.

Here the trains are moving in the same directions then their

Relative speed = 101 - 90 = 11 miles per hour

Distance between them = 42 - 6 = 36 miles

So the time to cover up this distance by the trains will be

Speed = distance/ time Or time = distance/speed

time = 36/11 = 3.27 hours

Therefore answer is 3.27 hours

0,0(0 оценок)