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Usimov [2.4K]
3 years ago
8

What is the minimum amount that must be on hand?

Mathematics
1 answer:
Arturiano [62]3 years ago
6 0
Sent a picture of the solution to the problem (s).

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3.
Vitek1552 [10]
To solve this we are going to use the future value of annuity due formula: FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]
where
FV is the future value
P is the periodic deposit 
r is the interest rate in decimal form 
n is the number of times the interest is compounded per year
k is the number of deposits per year

We know for our problem that P=420 and t=15. To convert the interest rate to decimal form, we are going to divide the rate by 100%: r= \frac{10}{100} =0.1. Since Ruben makes the deposits every 6 months, k=2. The interest is compounded semiannually, so 2 times per year; therefore, k=2.
Lets replace the values in our formula:

FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]
FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ]
FV=29299.53

We can conclude that the correct answer is <span>$29,299.53</span>
8 0
3 years ago
Which equation shows function notation for a vertical stretch of factor 2 and shift right 5 units? *
liubo4ka [24]

Answer: I am doing an giveaway for and iphone 11 pro max (black)

Step-by-step explanation: first person who message me gets it be the first

7 0
3 years ago
7.60. When Paul crossed the finish line of a 60-meter race, he was ahead of Robert by 10 meters and ahead of Sam by 20 meters. S
Lelechka [254]

Answer:

The number of meters Robert will beat Sam is 12 meters.

Step-by-step explanation:

Given:

When Paul crossed the finish line of a 60-meter race, he was ahead of Robert by 10 meters and ahead of Sam by 20 meters. Suppose Robert and Sam continue to race to the finish line without changing their rates of speed.

Find:

the number of meters by which Robert will beat Sam

Step 1 of 1

When Paul finishes, Robert has run 60-10=50 meters and Sam has run 60-20=40 meters.

Therefore, when Robert and Sam run for the same amount of time, Sam covers $\frac{40}{50}=\frac{4}{5}$ of the distance that Robert covers. So, while Robert runs the final 10 meters of the race, Sam runs $\frac{4}{5} \cdot 10=8$ meters.

This means Robert's lead over Sam increases by 2 more meters, and he beats Sam by 10+2=12 meters.

5 0
2 years ago
Two pools are being drained. To start, the first pool had 3850 liters of water and the second pool had 4370 liters of water. Wat
SashulF [63]

Answer:

(a)

Amount of water in the first pool (in liters) = 3850 liters - 33 liters per minute * x minutes

Amount of water in the second pool (in liters) = 4370 liters - 43 liters per minute * x minutes

(b)

3850 liters - 33 liters per minute * x minutes= 4370 liters - 43 liters per minute * x minutes

Step-by-step explanation:

(a) With x being the minutes after which you want to calculate the amount of water in the pool, to calculate this amount of water you must subtract the water drained from the initial amount of water that the pool contains.

Knowing that, for example, the water from the first pool drains at a rate of 33 liters per minute, then after x minutes, the total water drained will be 33 liters per minute * x minutes. Then:

<u><em>Amount of water in the first pool (in liters) = 3850 liters - 33 liters per minute * x minutes</em></u>

Reasoning in the same way:

<u><em>Amount of water in the second pool (in liters) = 4370 liters - 43 liters per minute * x minutes</em></u>

(b)  Now want to know when the two pools would have the same amount of water.  If they have the same amount of water then you can express:

Amount of water in the first pool = Amount of water in the second pool

Replacing the expressions found in (a):

<u><em>3850 liters - 33 liters per minute * x minutes= 4370 liters - 43 liters per minute * x minutes</em></u>

5 0
3 years ago
I need help fast! I’m taking the test now!
Zina [86]

Answer:

it's the last one I think

6 0
2 years ago
Read 2 more answers
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