2. 1- =[?]× -
3 3
What number makes the equation true? Enter the answer in the box.​

Answer:

  b) $17,400

  d) $33,517.20

Step-by-step explanation:

a) $28,482.19 . . . . future value of all deposits

__

b) The initial deposit was $3000, and there were 144 deposits of $100 each, for a total of ...

  $3000 +144×100 = $17,400 . . . . total deposited

__

c) $558.62

__

d) 60 monthly withdrawals were made in the amount $558.62, for a total of ...

  60×$558.62 = $33,517.20 . . . . total withdrawn

_____

Additional information about (a) and (c)

(a) The future value of the initial deposit is the deposit multiplied by the interest multiplier over the period.

  A = P(1 +r/n)^(nt) = 3000(1 +.066/12)^(12·12) = 3000·1.0055^144 ≈ 6609.065

The future value of $100 deposits each month is the sum of the series of 144 terms with common ratio 1.0055 and initial value 100.

  A = 100(1.055^144 -1)/0.0055 ≈ 21,873.123

So, the total future value is ...

  $6609.065 +21873.123 ≈ $28482.188 ≈ $28,482.19

__

(c) The withdrawal amount can be found using the same formula used for loan payments:

  A = P(r/n)/(1 -(1 +r/n)^(-nt)) = $28482.19(.0055)/(1 -1.0055^-60) ≈ $558.62

Final answer:

The total amount deposited in the account was $17,400 including an initial investment of $3,000 and subsequent monthly payments of $100 for 12 years. The total amount withdrawn was equal to the final balance after the last deposit.

Explanation:

Let's tackle each question one by one:

1. You've mentioned that you have already figured out part (a) and (c), so let's move on to part (b).
2. (b) How much was deposited?The individual started with an initial deposit of $3,000. After that, they deposited $100 at the end of each month for 12 years. That's 12 years * 12 months/year * $100/month, for a total of $14,400. So, if you add the initial deposit, the total amount deposited over the whole period is $3,000 + $14,400 = $17,400.
3. (d) What is the total amount withdrawn?The total amount withdrawn is the same as the final balance of the account after the last deposit, as the question states the account balance will be zero after the withdrawals. Since you have already figured out part (a) which is the account balance after the last deposit, the total amount withdrawn corresponds to that sum.

Learn more about Compound Interest here:

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Answer:

x = 25

Measure of each angle label is 42°

Step-by-step explanation:

(x + 17)° and (3x - 33)° are the expressions of the two vertical angles formed by the intersection of two straight lines. Vertical opposite angles are congruent. Therefore:

x + 17 = 3x - 33

Solve for x. Collect like terms

17 + 33 = 3x - x

50 = 2x

Divide both sides by 2

50/2 = 2x/2

25 = x

Measure of the two angles are:

x + 17 = 25 + 17 = 42° (substitution)

3x - 33 = 3(25) - 33 = 75 - 33 = 42°

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

Let = average calorie content of a 12-ounce can.

So, Null Hypothesis, : 120 calories     {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, : > 120 calories     {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                         T.S. =    ~

where, = sample average calories per can = 124 calories

             s = sample standard deviation = 6 calories

            n = sample of cans = 10

So, test statistics  =    ~

                               =  2.108

The value of t test statistics is 2.108.

Now, at 0.05 significance level the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Answer:

111°

Step-by-step explanation:

By exterior angle theorem:

Answer:

x = 111

Step-by-step explanation:

180- 82 -29 is 69 and 180-69 is x which x is equal to 111

Answer:

Step-by-step explanation:

√6 + 3√6 = 4√6

Hope this helps

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Answer:

Risk taking

Vision driven

Passionate

Goal oriented

Decision maker.

Step-by-step explanation:

An entrepreneur is a person who sets up a business, manages it and work towards maximizing profit.

In order to be able to navigate the "new normal", these five qualities are very essential in an entrepreneur if he/she wishes to go far.

Answer:

1. Integrity

2. Self discipline

3. Clear sense of direction

4 . Persistence

5. Action oriented and decisive

Step-by-step explanation:

1. Integrity can be define as the practice of being honest and showing a consistent and uncompromising adherence to strong moral and ethical principles and values.

2. Self discipline or Self-control, can be described as an aspect of inhibitory control, is the ability to regulate one's emotions, behavior and thought in the face of temptations and impulses.

3.. When have a clear sense if direction, we mean that person seem to have clear ideas about what they want to do or achieve.

4. When we say someone who is persistent, that person continues doing something or tries to do something in a determined but often unreasonable way.

5. Action oriented and decisive can be define as an action or actions done quickly and with confidence. How to use decisive action in a sentence.