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algol13
3 years ago
9

A leaking faucet drips into a bucket. The faucet drips at a constant rate. The level of water in the bucket rises

Mathematics
1 answer:
Sveta_85 [38]3 years ago
7 0

Answer:

The per hour rate is 0.5 inches per hour

Step-by-step explanation:

Here, we want to calculate the rate at which the level of the water increased

Mathematically, we can get this by dividing the amount of increment by the time it took

That would be 3 inches divided by 6 hours

= 3/6 = 0.5 inches per hour

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On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter
andrezito [222]

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0
3 years ago
Find the 4th term <br><br> Thank you in advance
shepuryov [24]
B1 = 2
b2 = (b1)^2 + 1 = 2^2 + 1 = 5
b3 = (b2)^2 + 1 = 5^2 + 1 = 26

b4 = (b3)^2 + 1 = 26^2 + 1 = 676+1=<span>677</span>
7 0
3 years ago
Read 2 more answers
"Which ranges describe the cluster in the scatter plot?
Minchanka [31]
A.between 8 and 10 years of age,
<span>C.between 10 and 12 years of age

</span>

7 0
3 years ago
Read 2 more answers
A computer online service charges one hourly rate for regular use but a higher hourly rate for designated "premium" areas. One c
N76 [4]

Answer: the service charge per hour for premium services is $5.5

the service charge per hour for regular services is $3

Step-by-step explanation:

Let x represent the service charge per hour for premium services.

Let y represent the service charge per hour for regular services.

One customer was charged $38 after spending 2 h in premium areas and 9 regular hours. It means that

2x + 9y = 38- - - - - - - - - - - 1

Another customer spent 3 h in premium areas and 6 regular hours and was charged $34.50. It means that

3x + 6y = 34.5- - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 2. It becomes

6x + 27y = 114

6x + 12y = 69

Subtracting, it becomes

15y = 45

y = 45/15

y = 3

Substituting y = 3 into equation 1, it becomes

2x + 9 × 3 = 38

2x + 27 = 38

2x = 38 - 27 = 11

x = 11/2 = 5.5

8 0
3 years ago
6. Carrie buys 4.16 pounds of apples for $5.20.<br> How much does 1 pound cost?
spayn [35]
$1.25
Hope I helped !!
8 0
2 years ago
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