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Karo-lina-s [1.5K]
3 years ago
10

1. Jenna makes $96,000 per year working for an online e-magazine. Her company offers a 401K retirement plan in which they will m

atch 45% of her contributions
to the 401K up to 9% of her salary. The company will only allow employees to make contributions to the 401K to a maximum of 25% of their salary. For the year
in question, the maximum allowable contribution to any 401K is $22,000 since she is over the age of 55.
a) What is the maximum Jenna's employer will allow for her contribution?
b) What is the maximum contribution she could make?
c) What is her employer's maximum contribution amount?
Mathematics
1 answer:
Nikolay [14]3 years ago
3 0

Answer:

a) The maximum Jenna's employer will allow for her contribution is $24,000.

b) The maximum contribution she could make is $22,000.

c) Her employer's maximum contribution amount is $8,640.

Step-by-step explanation:

a) What is the maximum Jenna's employer will allow for her contribution?

The maximum Jenna's employer will allow for her contribution = Jenna's annual salary * Maximum percentage allowed by her employer = $96,000 * 25% = $24,000

b) What is the maximum contribution she could make?

The maximum contribution she could make = The maximum allowable contribution to any 401K for the year in question = $22,000

c) What is her employer's maximum contribution amount?

Her employer's maximum contribution amount = Jenna's annual salary * 9% = $96,000 * 9% = $8,640

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Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.
laila [671]

Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is  (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

  • if |a|> b then a>b or a<-b
  • if |a|< b then a<b or a>-b

So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

6 0
3 years ago
A two-digit number becomes 5/6 of the reversed number obtained when the digits are interchanged. The difference between the digi
stealth61 [152]
<h3>Answer:   54</h3>

==============================================

Work Shown:

T = tens digit

U = units digit (aka ones digit)

A number like 27 is really 20+7 = 2*10 + 7*1 = 10*2 + 1*7. We have 2 in the tens digit and 7 in the units digit. So 27 can be written in the form 10T + U where T = 2 and U = 7. Reversing the digits gives 72, so T = 7 and U = 2 now. Clearly the difference between the digits 7 and 2 is not 1, so 27 or 72 is not the answer (as it's just an example).

-----------------------

Let T be larger than U. This doesn't work if T = U.

Because T is larger, saying "The difference between the digits is 1" means T - U = 1. We can isolate T to get T = U+1. We'll use this later.

-----------------------

If T > U, then the original number 10T+U reverses to the new number 10U+T and it becomes smaller. We are told that it becomes 5/6 of what it used to be.

So,

new number = (5/6)*(old number)

10U + T = (5/6)(10T + U)

6(10U + T) = 5(10T + U)

60U + 6T = 50T + 5U

60U + 6(U+1) = 50(U+1) + 5U ... plug in T = U+1

60U + 6U + 6 = 50U + 50 + 5U

66U + 6 = 55U + 50

66U - 55U = 50-6

11U = 44

U = 44/11

U = 4 is the units digit of the original number

T = U+1

T = 4+1

T = 5 is the tens digit of the original number

The original number is therefore 10T + U = 10*5+4 = 54.

We see the difference in their digits is T-U = 5-4 = 1

The reverse of 54 is 45. The number 45 is 5/6 of 54

45 = (5/6)*54

7 0
3 years ago
What is the <img src="https://tex.z-dn.net/?f=%5Csqrt%7B10%7D" id="TexFormula1" title="\sqrt{10}" alt="\sqrt{10}" align="absmidd
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6.32455532 is what my calculator says.
4 0
3 years ago
|5x-4|&gt;16 solutions
lions [1.4K]

Answer:

x >4                         or            x < -12/5

Step-by-step explanation:

An absolute value has 2 solutions, a positive and a negative.  Remember to flip the inequality for the negative solution

|5x-4|>16

5x-4 > 16        5x-4 < -16

Add 4 to each side

5x-4 +4> 16+4   or     5x-4+4 < -16+4

5x > 20                or        5x < -12

Divide each side by 5

5x/5 > 20/5          or         5x/5 < -12/5

x >4                         or            x < -12/5

5 0
3 years ago
You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
anyanavicka [17]

9514 1404 393

Answer:

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  • repaid: $378,000
  • interest: $220,177

Step-by-step explanation:

For a loan value of 1, the monthly payment on a 30 year loan at 7% is ...

  A = (0.07/12)/(1 -(1 +0.07/12)^(-12·30)) ≈ 0.00665302495

Then the amount repaid after 360 payments is ...

  360A = 2.39508898 . . . times the principal amount

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a) For a monthly payment of $1050, the principal can be ...

  $1050/0.00665302495 ≈ $157,823

__

b) The amount repaid to the loan company is ...

  $157,823×2.39508898 ≈ $378,000

__

c) The amount that is interest is ...

  $378,000 -157,823 = $220,177

8 0
3 years ago
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