Answer:
$2500 at 8%.
$2900 st 5%.
Step-by-step explanation:
Let x be the amount invested at rate of 8% and y be the amount invested at the rate of 5%.
We have been given that Heather has divided $5400 between two investments. We can represent this information as:
The return on her investment is $345.
Earnings from the investment at 8% will be 8% of x.
Earnings from the investment at 5% will be 5% of y.
We will use substitution method to solve our system of equations. From equation (1) we will get,
Substituting this value in equation (2) we will get,
Therefore, Heather has invested an amount of $2900 at 5%.
Let us substitute y=2900 in equation (1) to solve for x.
Therefore, Heather has invested an amount of $2500 at 8%.
You could use the information from part A to get B. I'm not sure if you want A or not, so I'll do it as well.
A
Eo = 10^4.4 Joules
E = 2 * 10^15
Formula
M = (2/3) log (E/Eo)
M = 2/3 * log (2 * 10^15/10^(4.4) )
M = 2/3 * log( 7.9621* 10^10)
M = 2/3 * 10.901
M = 7.26735 on the Richter scale. That is a huge amount of energy.
Part B
Suppose that you use Eo and your base. Eo is 10^4.4
Now the new earthquake is E = 10000 * Eo
So what you get now is M = (2/3)* Log(10000 * Eo / Eo )
The Eo's cancel out.
M = 2/3 * log(10000)
M = 2/3 of 4
M = 8/3
M = 2.6667 difference in the Richter Scale Reading. It is still an awful lot of energy.
What this tells you is that if the original reading was (say) 6 then the 10000 times bigger reading would 8.266667
Answer: M = 2.6667
Answer:
Kristi
Step-by-step explanation:
The formula for Simple Interest =
Principal × Rate × Time
For Kristi
Kristi invests $3,000 at a 7.25% annual simple interest rate,
Principal = $3000
Rate = 7.25% = 0.0725
Time = 1
Simple interest = $3000 × 0.0725 × 1
= $217.5
For Kari
Her sister Kari invests $3,200 at a 6.25% annual simple interest rate.
Principal = $3200
Rate = 6.25% = 0.0625
Time = 1
Simple interest = $3200 × 0.0625 × 1
= $200
From the above calculation, we can see that: Kristi will earn the greater amount of interest after one year
Answer:
1.75 gallons
Step-by-step explanation:
First, we need to calculate how far the hike is going up the trail. They first hike 2 miles and then another 1.75 miles after resting so...
2 + 1.75 = 3.75 miles
The trail is 3.75 miles long, the question states that the return path is 0.5 miles shorter, therefore...
3.75 - 0.5 = 3.25 miles
Leaving us with a total hiking distance of
3.75 + 3.25 = 7 miles.
Since each hiker will carry 0.25 gallons for each mile we simply need to multiply this amount by the total number of miles in the hike.
7 * 0.25 = 1.75 gallons
Finally, we can see that each hiker will carry a total of 1.75 gallons of water for the entire hike.
Answer:
112
Step-by-step explanation:
