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Lelu [443]
2 years ago
7

Linda Davis agreed to lend money to Alex Luciano at a special interest rate of ​9% per​ year, on the condition that he borrow en

ough that he would pay her ​$400 in interest over a ​-year period. What was the minimum amount Alex could​ borrow?
Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
4 0

9514 1404 393

Answer:

  $4444.44

Step-by-step explanation:

The amount of interest on a given principal is found by ...

  I = Prt . . . . principal P earning annual rate r for t years.

We want ...

  400 = P×0.09×1

  P = 400/0.09 ≈ 4444.44

Alex needs to borrow $4444.44.

_____

<em>Additional comment</em>

For exactly $400 in interest, the amount is not an integral number of cents, so some rounding of interest or loan amount must occur. In that case, the minimum to borrow is that which will give a calculated interest of at least $399.995. That amount is $399.994/0.09 ≈ $4444.3888.... ≈ $4444.39. Alex can borrow a minimum of $4444.39 and still have to pay $400 in interest.

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Suppose that 12% of test scores for the unit 1 test were above 85 and 8% were below 70. Assuming a normal
Doss [256]

Answer:

Mean = 78.2

Standard deviation = 5.8

Step-by-step explanation:

Mathematically z-score;

= (x-mean)/SD

From the question;

12% of test scores were above 85

Thus;

P( x > 85) = 12%

P(x > 85) = 0.12

Now let’s get the z-score that has a probability of 0.12

This can be obtained from the standard normal distribution table and it is = 1.175

Thus;

1.175 = (85 - mean)/SD

let’s call the mean a and the SD b

1.175 = (85-a)/b

1.175b = 85 - a

a = 85 - 1.175b ••••••••(i)

Secondly 8% of scores were below 70

Let’s find the z-score corresponding to this proportion;

We use the standard normal distribution table as usual;

P( x < 70) = 0.08

z-score = -1.405

Thus;

-1.405 =( 70-a)/b

-1.405b = 70-a

a = 70 + 1.405b ••••••(ii)

Equate the two a

70 + 1.405b = 85 - 1.175b

85 -70 = 1.405b + 1.175b

15 = 2.58b

b = 15/2.58

b = 5.81

a = 70 + 1.405b

a = 70 + 1.405(5.81)

a = 78.16

So mean = 78.2 and Standard deviation is 5.8

4 0
3 years ago
Closed circle on 2 to closed circle on 6
Stella [2.4K]

Answer:

see the explanation

Step-by-step explanation:

we have

closed circle on 2 to closed circle on 6

That means -----> All real numbers greater than or equal to 2 and less than or equal to 6

In interval notation is ------> [2,6]

In set builder notation is ----> { x ∈ R | x ≥ 2 and x ≤ 6 }

7 0
3 years ago
The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t4 – 10t3 + 28t2 – 24t, where t i
vekshin1

In this question, the profit of the restaurant after t months is given by a polynomial function. To find when it begins to show a profit, we find the numerical values of the function for t, and it shows a profit when t > 0

Profit after t months:

P(t) = t^4 - 10t^3 + 28t^2 - 24t

0 months:

This is P(0). So

P(0) = 0^4 - 10*0^3 + 28*0^2 - 24*0 = 0

1 month:

This is P(1). So

P(1) = 1^4 - 10*1^3 + 28*1^2 - 24*1 = -5

2 months:

This is P(2). So

P(2) = 2^4 - 10*2^3 + 28*2^2 - 24*2 = 0

3 months:

This is P(3). So

P(3) = 3^4 - 10*3^3 + 28*3^2 - 24*3 = -9

4 months:

This is P(4). So

P(4) = 4^4 - 10*4^3 + 28*4^2 - 24*4 = -32

5 months:

This is P(5). So

P(5) = 5^4 - 10*5^3 + 28*5^2 - 24*5 = -45

6 months:

This is P(6). So

P(6) = 6^4 - 10*6^3 + 28*6^2 - 24*6 = 0

7 months:

This is `P(7). So

P(7) = 7^4 - 10*7^3 + 28*7^2 - 24*7 = 175

After 7 months it shows profit, so it starts showing profit on the 6th month, and thus, the correct answer is given by option D.

For another example of a function involving numeric value, you can check brainly.com/question/24231879

8 0
3 years ago
I solved 12 I need help with 13 plzzzzzz
nataly862011 [7]

Answer:

8.75:1

Step-by-step explanation:

i could be wrong but im pretty sure

3 0
2 years ago
Read 2 more answers
I need help on this question
Paul [167]
9P2 =72

= 9!/ (9-2)!
4 0
3 years ago
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