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goblinko [34]
3 years ago
13

Daniel opens a savings account and deposits $100 into it. Each year, the amount of money in his account increases by 5%. Use the

drop-down menus to complete an inequality that can be solved to find how much time, t, it will take for there to be at least $500 in Daniel's account.
Mathematics
2 answers:
shtirl [24]3 years ago
5 0

it will take him 33 years to reach $500

Alina [70]3 years ago
4 0

Answer:

500\leq 100(1.05)^t

Step-by-step explanation:

Given,

The initial deposit, P = $ 100,

Annual increasing rate, r = 5 %,

Thus, the amount after t years,

A=P(1+\frac{r}{100})^t

=100(1+\frac{5}{100})^t

=100(1+0.05)^t

\implies A = 100(1.05)^t

According to the question,

A ≥ $ 500

\implies 500\leq 100(1.05)^t

Which is the required inequality that can be used the value of t.

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Suppose y varies directly with x. If y = 4 when x = -2, find x when y = 6.
daser333 [38]

Answer:

Step-by-step explanation:

3 0
3 years ago
if a runner finishes the 26.2. mille race in 4 hours and 37 mins and Wilson kipping finish in 4 minutes and 43 seconds per mile
Neporo4naja [7]

Answer

a) Wilson Kipsang is 7.046 miles per hour faster than the average runner.

Solution is presented below under Explanation.

b) Wilson Kipsang is 2.24 times faster than the average runner.

c) When the average runner is at mile 6, Kipsang will be at mile 13.45.

d) Kipsang's record time = 2 hours, 3 minutes, 34.6 seconds

Explanation

To solve this, we will calculate the speed of the average runner and then the speed of Wilson Kipsang

Speed = (Distance/Time)

For the average runner

Distance = 26.2 miles

Time = 4 hours 37 mins = 4 hours + (37/60) = 4.617 hours

Speed = (Distance/Time)

Speed = (26.2/4.617)

Speed = 5.675 miles per hour

For Wilson Kipsang

Distance = 1 mile

Time = 4 minutes 43 seconds = (4/60) + (43/3600) = 0.0667 + 0.01194 = 0.0786 hour

Speed = (Distance/Time)

Speed = (1/0.0786) = 12.721 miles per hour

So, now, we are asked to find how much faster than the average runner is Wilson Kipsang

Wilson Kipsang's speed = 12.721 miles per hour

Average runner's speed = 5.675 miles per hour

Wilson Kipsang is faster than the average runner by

(12.721 - 5.676) = 7.046 miles per hour

b) We are asked to find how many times faster than the average runner Wilson Kipsang is.

Let the number of times he is faster than the average runner be x

Wilson Kipsang's speed = 12.721 miles per hour

Average runner's speed = 5.675 miles per hour

(5.675) (x) = (12.721)

Divide both sides by 5.675

x = (12.721/5.675)

x = 2.24 times

c) If the average runner is at mile 6, where would Kipsang be?

To do this, we will find the time it takes the average runner to be at mile 6, then use that time to find where Kipsang would be.

Speed = (Distance/Time)

By cross multiplying, we see that

Time = (Distance/Speed)

For the average runner

Distance = 6 miles

Speed = 5.675 miles per hour

Time = (Distance/Speed)

Time = (6/5.675) = 1.057 hours

For Wilson Kipsang,

Speed = (Distance/Time)

By cross multiplying

Distance = (Speed) (Time)

Speed = 12.721 miles per hour

Time = 1.057 hours

Distance = (Speed) (Time)

Distance = (12.721) (1.057)

Distance = 13.45 miles

d) We were told that for Kipsang

1 mile = 4 minutes 43 seconds

26.2 miles = 26.2 (4 minutes 43 seconds)

26.2 miles = 26.2 (283 seconds) = 7414.6 seconds

We can then convert this further

7414.6 seconds = 2 hours, 3 minutes, 34.6 seconds

Hope this Helps!!!

4 0
1 year ago
Consider the line y = 2/3x-4
motikmotik

Answer:

For the parallel line it will still have a slpoe of 2/3

Step-by-step explanation:

as for the perpendicular line it will be double like 4/6 so it can meet it at a 90° angle.

5 0
3 years ago
Find the value of 5.8 ÷ 1.2.
EastWind [94]
Your answer is 4.83
5 0
3 years ago
4. There are seven days in a week. How many days are there in 16 weeks?
lesya692 [45]

Answer:

There are 112 days in 16 weeks

8 0
3 years ago
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